- FindStat

Your data matches 108 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001704

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001704: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 4
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 4
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 4
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3

Description

The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. The deck of a graph is the multiset of induced subgraphs obtained by deleting a single vertex. The graph reconstruction conjecture states that the deck of a graph with at least three vertices determines the graph. This statistic is only defined for graphs with at least two vertices, because there is only a single graph of the given size otherwise.

Matching statistic: St001734

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001734: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 80%●distinct values known / distinct values provided: 67%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4

Description

The lettericity of a graph. Let $D$ be a digraph on $k$ vertices, possibly with loops and let $w$ be a word of length $n$ whose letters are vertices of $D$. The letter graph corresponding to $D$ and $w$ is the graph with vertex set $\{1,\dots,n\}$ whose edges are the pairs $(i,j)$ with $i < j$ sucht that $(w_i, w_j)$ is a (directed) edge of $D$.

Matching statistic: St001572

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001572: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 80%●distinct values known / distinct values provided: 67%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1

Description

The minimal number of edges to remove to make a graph bipartite.

Matching statistic: St001573

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001573: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 80%●distinct values known / distinct values provided: 67%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 1
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 1

Description

The minimal number of edges to remove to make a graph triangle-free.

Matching statistic: St001577

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001577: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 80%●distinct values known / distinct values provided: 67%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 2 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 2
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 - 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 - 2
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 - 2
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 - 2

Description

The minimal number of edges to add or remove to make a graph a cograph. A cograph is a graph that can be obtained from the one vertex graph by complementation and disjoint union.

Matching statistic: St001812

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001812: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 64%●distinct values known / distinct values provided: 33%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3

Description

The biclique partition number of a graph. The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph $K_n$ has biclique partition number $n - 1$.

Matching statistic: St001703

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001703: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 59%●distinct values known / distinct values provided: 33%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 + 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 + 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 + 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 + 2
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 + 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3 + 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 + 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4 + 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 + 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3 + 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 + 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 + 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4 + 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 + 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4 + 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 + 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4 + 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 + 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 + 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 + 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 + 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 + 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 + 2

Description

The villainy of a graph. The villainy of a permutation of a proper coloring $c$ of a graph is the minimal Hamming distance between $c$ and a proper coloring. The villainy of a graph is the maximal villainy of a permutation of a proper coloring.

Matching statistic: St001644

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001644: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 55%●distinct values known / distinct values provided: 33%

Values

([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2

Description

The dimension of a graph. The dimension of a graph is the least integer $n$ such that there exists a representation of the graph in the Euclidean space of dimension $n$ with all vertices distinct and all edges having unit length. Edges are allowed to intersect, however.

Matching statistic: St000259

Mapping

Mp00111: Graphs —complement⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 33%

Values

([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ? = 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ? = 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ? = 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ? = 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ? = 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ? = 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ? = 4
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(4,5)],6)
 => ? = 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St000046

Mapping

Mp00111: Graphs —complement⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000046: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 33%

Values

([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => ? = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 4 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 4 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1]
 => 1 = 2 - 1

Description

The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition.

The following 98 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000137The Grundy value of an integer partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000260The radius of a connected graph. St000456The monochromatic index of a connected graph. St000460The hook length of the last cell along the main diagonal of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000781The number of proper colouring schemes of a Ferrers diagram. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001360The number of covering relations in Young's lattice below a partition. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001383The BG-rank of an integer partition. St001389The number of partitions of the same length below the given integer partition. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001561The value of the elementary symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001571The Cartan determinant of the integer partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001763The Hurwitz number of an integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001943The sum of the squares of the hook lengths of an integer partition. St000145The Dyson rank of a partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000699The toughness times the least common multiple of 1,. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001176The size of a partition minus its first part. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001280The number of parts of an integer partition that are at least two. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001541The Gini index of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001961The sum of the greatest common divisors of all pairs of parts. St000474Dyson's crank of a partition. St000454The largest eigenvalue of a graph if it is integral. St000422The energy of a graph, if it is integral.