- FindStat

Your data matches 57 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000552
(load all 7 compositions to match this statistic)

Mapping

St000552: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

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

Description

The number of cut vertices of a graph. A cut vertex is one whose deletion increases the number of connected components.

Matching statistic: St000362
(load all 3 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000362: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 97%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(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)
 => 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ?
 => ? = 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,6),(3,6),(3,9),(4,7),(4,9),(5,8),(5,9)],10)
 => ?
 => ? = 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
 => ?
 => ? = 5
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
 => ?
 => ? = 4

Description

The size of a minimal vertex cover of a graph. A '''vertex cover''' of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. Finding a minimal vertex cover is an NP-hard optimization problem.

Matching statistic: St000387
(load all 3 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000387: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 97%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(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)
 => 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ?
 => ? = 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,6),(3,6),(3,9),(4,7),(4,9),(5,8),(5,9)],10)
 => ?
 => ? = 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
 => ?
 => ? = 5
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
 => ?
 => ? = 4

Description

The matching number of a graph. For a graph $G$, this is defined as the maximal size of a '''matching''' or '''independent edge set''' (a set of edges without common vertices) contained in $G$.

Matching statistic: St000985
(load all 2 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000985: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 97%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(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)
 => 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ?
 => ? = 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,6),(3,6),(3,9),(4,7),(4,9),(5,8),(5,9)],10)
 => ?
 => ? = 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
 => ?
 => ? = 5
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
 => ?
 => ? = 4

Description

The number of positive eigenvalues of the adjacency matrix of the graph.

Matching statistic: St001459

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
St001459: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 97%●distinct values known / distinct values provided: 67%

Values

([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => 0
([(0,1)],2)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => 0
([(1,2)],3)
 => ([],2)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => 0
([(2,3)],4)
 => ([],3)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => 0
([(3,4)],5)
 => ([],4)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3)],5)
 => ([],3)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => 0
([(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)
 => ? = 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ? = 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ? = 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ? = 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ? = 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ? = 4
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ? = 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,6),(3,6),(3,9),(4,7),(4,9),(5,8),(5,9)],10)
 => ? = 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
 => ? = 5
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
 => ? = 4

Description

The number of zero columns in the nullspace of a graph.

Matching statistic: St001812
(load all 3 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001812: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 95%●distinct values known / distinct values provided: 50%

Values

([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => 0
([(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)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(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)
 => ? = 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(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)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => 0
([(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)
 => ? = 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(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),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(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),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 3
([(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),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 3
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ?
 => ? = 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
 => ?
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ([(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)
 => ? = 3
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => ([(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)
 => ? = 3
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,6),(3,6),(3,9),(4,7),(4,9),(5,8),(5,9)],10)
 => ?
 => ? = 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
 => ?
 => ? = 5
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(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)
 => ? = 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: St001581

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001581: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 95%●distinct values known / distinct values provided: 50%

Values

([],1)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,2)],3)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 1 + 2
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 1 + 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)
 => 3 = 1 + 2
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 4 = 2 + 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 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)
 => 3 = 1 + 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)
 => 3 = 1 + 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)
 => 3 = 1 + 2
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 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 + 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)
 => 3 = 1 + 2
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 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)
 => 4 = 2 + 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)
 => 3 = 1 + 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)
 => 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 4 = 2 + 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)
 => 3 = 1 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 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)
 => ? = 3 + 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 4 = 2 + 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)
 => 3 = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 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)
 => ? = 3 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(0,8),(1,5),(1,8),(2,7),(2,8),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 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)
 => ? = 3 + 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(0,9),(1,7),(1,9),(2,3),(2,4),(2,9),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
 => ? = 4 + 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)
 => ? = 3 + 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)
 => ? = 3 + 2
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2 + 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2 + 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2 + 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2 + 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3 + 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2 + 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3 + 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2 + 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 3 + 2
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3 + 2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3 + 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3 + 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4 + 2
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 + 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 + 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4 + 2
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ?
 => ? = 3 + 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ?
 => ? = 4 + 2
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
 => ?
 => ? = 3 + 2
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(0,8),(1,5),(1,8),(2,7),(2,8),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(0,9),(1,7),(1,9),(2,3),(2,4),(2,9),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
 => ? = 4 + 2
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,8),(1,7),(2,6),(3,6),(3,9),(4,7),(4,9),(5,8),(5,9)],10)
 => ?
 => ? = 4 + 2
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(0,8),(1,5),(1,8),(2,7),(2,8),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
 => ?
 => ? = 5 + 2
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(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)
 => ? = 3 + 2

Description

The achromatic number of a graph. This is the maximal number of colours of a proper colouring, such that for any pair of colours there are two adjacent vertices with these colours.

Matching statistic: St001734
(load all 5 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
St001734: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 93%●distinct values known / distinct values provided: 50%

Values

([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 1 = 0 + 1
([],4)
 => ([],4)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3 = 2 + 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 1 = 0 + 1
([],5)
 => ([],5)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 3 = 2 + 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2 = 1 + 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 3 = 2 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2 = 1 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 3 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ? = 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)
 => ? = 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)
 => ? = 3 + 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)
 => ? = 2 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3 + 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)
 => ? = 3 + 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 4 + 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)
 => ? = 3 + 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)
 => ? = 3 + 1
([],7)
 => ([],7)
 => ? = 0 + 1
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ? = 1 + 1
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ? = 1 + 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1 + 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1 + 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)
 => ? = 1 + 1
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ? = 2 + 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2 + 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2 + 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ? = 2 + 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ? = 3 + 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ? = 2 + 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 2 + 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ? = 2 + 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ? = 3 + 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)
 => ? = 2 + 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ? = 2 + 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)
 => ? = 2 + 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ? = 3 + 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)
 => ? = 2 + 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ? = 3 + 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 2 + 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ? = 3 + 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ? = 2 + 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 2 + 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ? = 3 + 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)
 => ? = 2 + 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)
 => ? = 2 + 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ? = 4 + 1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ? = 3 + 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3 + 1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ? = 3 + 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ? = 4 + 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ? = 3 + 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ? = 4 + 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3 + 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3 + 1

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: St001670

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001670: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 93%●distinct values known / distinct values provided: 50%

Values

([],1)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,2)],3)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 1 + 2
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 1 + 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)
 => 3 = 1 + 2
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 4 = 2 + 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 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)
 => 3 = 1 + 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)
 => 3 = 1 + 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)
 => 3 = 1 + 2
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 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 + 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)
 => 3 = 1 + 2
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 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)
 => 4 = 2 + 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)
 => 3 = 1 + 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)
 => 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 4 = 2 + 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)
 => 3 = 1 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 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)
 => ? = 3 + 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 4 = 2 + 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)
 => 3 = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 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)
 => 3 = 1 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 3 + 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)
 => ? = 2 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(0,8),(1,5),(1,8),(2,7),(2,8),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 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)
 => ? = 3 + 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(0,9),(1,7),(1,9),(2,3),(2,4),(2,9),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
 => ? = 4 + 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)
 => ? = 3 + 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)
 => ? = 3 + 2
([],7)
 => ([],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 0 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 1 + 2
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2 + 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2 + 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 2 + 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 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)
 => ? = 2 + 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 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)
 => ? = 2 + 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)
 => ? = 2 + 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2 + 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3 + 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)
 => ? = 2 + 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2 + 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)
 => ? = 2 + 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
 => ?
 => ? = 3 + 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)
 => ? = 2 + 2
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 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)
 => ? = 2 + 2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3 + 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)
 => ? = 2 + 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)
 => ? = 2 + 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3 + 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)
 => ? = 2 + 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)
 => ? = 2 + 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4 + 2
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 + 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 + 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 + 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,9),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 4 + 2
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(0,6),(1,5),(2,4),(3,4),(5,7),(6,7)],8)
 => ?
 => ? = 3 + 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
 => ?
 => ? = 4 + 2
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3 + 2

Description

The connected partition number of a graph. This is the maximal number of blocks of a set partition $P$ of the set of vertices of a graph such that contracting each block of $P$ to a single vertex yields a clique. Also called the pseudoachromatic number of a graph. This is the largest $n$ such that there exists a (not necessarily proper) $n$-coloring of the graph so that every two distinct colors are adjacent.

Matching statistic: St001572

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001572: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 88%●distinct values known / distinct values provided: 50%

Values

([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0
([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 0
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0
([(1,2)],3)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 0
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 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
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(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
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(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
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 0
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 0
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0
([(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
([(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
([(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
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0
([(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)
 => ? = 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)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0
([(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)
 => ? = 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)
 => 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
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(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
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(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
([(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
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(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)
 => ? = 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(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
([(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
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(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
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 0
([(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
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 0
([],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 0
([(4,5)],6)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 0
([(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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 3
([(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)
 => ? = 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)
 => ? = 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)
 => ? = 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 3
([(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)
 => ? = 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(0,8),(1,5),(1,8),(2,7),(2,8),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 3
([(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)
 => ? = 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)
 => ? = 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)
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(0,9),(1,7),(1,9),(2,3),(2,4),(2,9),(3,5),(3,9),(4,6),(4,9),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)
 => ? = 4
([(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)
 => ? = 3
([(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)
 => ? = 3
([(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)
 => ? = 2
([],7)
 => ([],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 0
([(5,6)],7)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 0
([(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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 1
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],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)
 => ? = 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 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)
 => ? = 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)
 => ? = 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 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)
 => ? = 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)
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 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)
 => ? = 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)
 => ? = 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)
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 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)
 => ? = 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)
 => ? = 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
 => ?
 => ? = 3

Description

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

The following 47 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001573The minimal number of edges to remove to make a graph triangle-free. St001330The hat guessing number of a graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St001060The distinguishing index of a graph. St000264The girth of a graph, which is not a tree. St001570The minimal number of edges to add to make a graph Hamiltonian. 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. 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. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001432The order dimension of the partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. 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. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000699The toughness times the least common multiple of 1,.