Processing math: 100%

Your data matches 39 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000259
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],1)
 => 0
([],2)
 => ([],0)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],0)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],4)
 => ([],0)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 2
([],5)
 => ([],0)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 2
([],6)
 => ([],0)
 => ([],1)
 => 0
([(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St001393
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001393: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 96%●distinct values known / distinct values provided: 67%
Values
([],1)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
([],2)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],3)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],5)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
([(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 1 = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],6)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
([(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 0 = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 0 = 1 - 1
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],7)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 1
Description
The induced matching number of a graph. An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.
Matching statistic: St000455
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 78%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([],2)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 3
([],3)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 3
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([],4)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 3
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([],5)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 3
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 3
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ? = 1 - 3
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([],6)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 3
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 3
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ? = 1 - 3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? = 1 - 3
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 2 - 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 3
([],7)
 => ([],0)
 => ([],0)
 => ([],0)
 => ? = 0 - 3
([(5,6)],7)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 - 3
([(4,6),(5,6)],7)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 3
([(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ? = 1 - 3
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ? = 1 - 3
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],1)
 => ? = 1 - 3
([(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 3
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 3
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 3
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 2 - 3
Description
The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.
Matching statistic: St000264
(load all 7 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 61%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([],2)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([(0,1)],2)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([],3)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([(1,2)],3)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => [2,1] => ([(0,2),(1,2)],3)
 => ? = 1 + 1
([],4)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([(2,3)],4)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 2 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 2 + 1
([],5)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([(3,4)],5)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 + 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 2 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 1
([],6)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([(4,5)],6)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => [1,1] => ([(0,1)],2)
 => ? = 1 + 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 + 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 + 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 2 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 2 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 2 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 2 + 1
([],7)
 => ([],1)
 => [1] => ([],1)
 => ? = 0 + 1
([(5,6)],7)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(4,6),(5,6)],7)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
([(3,6),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => [1,2] => ([(1,2)],3)
 => ? = 1 + 1
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St001570
(load all 3 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 44%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 2
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 2
([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 2
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 2
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 1 - 2
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 2
([(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 2
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 - 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 2 - 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ? = 2 - 2
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 2
([(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 2
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 2 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 0 = 2 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ? = 2 - 2
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 2
([(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 1 - 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => ? = 1 - 2
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 1 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ? = 2 - 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ? = 2 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(3,6),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(2,3),(4,6),(5,6)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0 = 2 - 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0 = 2 - 2
Description
The minimal number of edges to add to make a graph Hamiltonian. A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.
Matching statistic: St001060
(load all 3 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 34%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ? = 0
([],2)
 => ([],1)
 => ([],1)
 => ? = 0
([(0,1)],2)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1
([],3)
 => ([],1)
 => ([],1)
 => ? = 0
([(1,2)],3)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ? = 1
([],4)
 => ([],1)
 => ([],1)
 => ? = 0
([(2,3)],4)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => ? = 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],1)
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ? = 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 2
([],5)
 => ([],1)
 => ([],1)
 => ? = 0
([(3,4)],5)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => ? = 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([],2)
 => ? = 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ? = 2
([],6)
 => ([],1)
 => ([],1)
 => ? = 0
([(4,5)],6)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([],2)
 => ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([],3)
 => ? = 2
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([],2)
 => ? = 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => ? = 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ? = 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([],2)
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ? = 2
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ? = 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => 2
Description
The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Matching statistic: St000618
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000618: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 33%
Values
([],1)
 => []
 => ?
 => ? = 0 - 1
([],2)
 => []
 => ?
 => ? = 0 - 1
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 1
([],3)
 => []
 => ?
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 1 - 1
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 1 - 1
([],4)
 => []
 => ?
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => ? = 1 - 1
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 2 - 1
([],5)
 => []
 => ?
 => ? = 0 - 1
([(3,4)],5)
 => [1]
 => []
 => ? = 1 - 1
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([],6)
 => []
 => ?
 => ? = 0 - 1
([(4,5)],6)
 => [1]
 => []
 => ? = 1 - 1
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 1 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
Description
The number of self-evacuating tableaux of given shape. This is the same as the number of standard domino tableaux of the given shape.
Matching statistic: St000781
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 33%
Values
([],1)
 => []
 => ?
 => ? = 0 - 1
([],2)
 => []
 => ?
 => ? = 0 - 1
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 1
([],3)
 => []
 => ?
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 1 - 1
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 1 - 1
([],4)
 => []
 => ?
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => ? = 1 - 1
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 2 - 1
([],5)
 => []
 => ?
 => ? = 0 - 1
([(3,4)],5)
 => [1]
 => []
 => ? = 1 - 1
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([],6)
 => []
 => ?
 => ? = 0 - 1
([(4,5)],6)
 => [1]
 => []
 => ? = 1 - 1
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 1 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
Description
The number of proper colouring schemes of a Ferrers diagram. A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1]. This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001432
(load all 2 compositions to match this statistic)
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001432: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 33%
Values
([],1)
 => []
 => ?
 => ? = 0 - 1
([],2)
 => []
 => ?
 => ? = 0 - 1
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 1
([],3)
 => []
 => ?
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 1 - 1
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 1 - 1
([],4)
 => []
 => ?
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => ? = 1 - 1
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 2 - 1
([],5)
 => []
 => ?
 => ? = 0 - 1
([(3,4)],5)
 => [1]
 => []
 => ? = 1 - 1
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([],6)
 => []
 => ?
 => ? = 0 - 1
([(4,5)],6)
 => [1]
 => []
 => ? = 1 - 1
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 1 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
Description
The order dimension of the partition. Given a partition λ, let I(λ) be the principal order ideal in the Young lattice generated by λ. The order dimension of a partition is defined as the order dimension of the poset I(λ).
Matching statistic: St001609
Mapping
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001609: Integer partitions ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 33%
Values
([],1)
 => []
 => ?
 => ? = 0 - 1
([],2)
 => []
 => ?
 => ? = 0 - 1
([(0,1)],2)
 => [1]
 => []
 => ? = 1 - 1
([],3)
 => []
 => ?
 => ? = 0 - 1
([(1,2)],3)
 => [1]
 => []
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => [2]
 => []
 => ? = 1 - 1
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => ? = 1 - 1
([],4)
 => []
 => ?
 => ? = 0 - 1
([(2,3)],4)
 => [1]
 => []
 => ? = 1 - 1
([(1,3),(2,3)],4)
 => [2]
 => []
 => ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2)],4)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => [3]
 => []
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => []
 => ? = 2 - 1
([],5)
 => []
 => ?
 => ? = 0 - 1
([(3,4)],5)
 => [1]
 => []
 => ? = 1 - 1
([(2,4),(3,4)],5)
 => [2]
 => []
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => [3]
 => []
 => ? = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => [3]
 => []
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => []
 => ? = 2 - 1
([],6)
 => []
 => ?
 => ? = 0 - 1
([(4,5)],6)
 => [1]
 => []
 => ? = 1 - 1
([(3,5),(4,5)],6)
 => [2]
 => []
 => ? = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5]
 => []
 => ? = 1 - 1
([(2,5),(3,4)],6)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(4,5)],6)
 => [3]
 => []
 => ? = 2 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(3,4),(3,5),(4,5)],6)
 => [3]
 => []
 => ? = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4]
 => []
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,5),(1,4),(2,3)],6)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(3,6),(4,5)],7)
 => [1,1]
 => [1]
 => 1 = 2 - 1
([(2,3),(4,6),(5,6)],7)
 => [2,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [2,2]
 => [2]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,5),(3,4)],7)
 => [1,1,1]
 => [1,1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => [2,1,1]
 => [1,1]
 => 1 = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,2]
 => [2]
 => 1 = 2 - 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [4,1]
 => [1]
 => 1 = 2 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => [3,1,1]
 => [1,1]
 => 1 = 2 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,1]
 => [1]
 => 1 = 2 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => [3,3]
 => [3]
 => 1 = 2 - 1
Description
The number of coloured trees such that the multiplicities of colours are given by a partition. In particular, the value on the partition (n) is the number of unlabelled trees on n vertices, [[oeis:A000055]], whereas the value on the partition (1n) is the number of labelled trees [[oeis:A000272]].
The following 29 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
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. 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. St001198The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001206The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St001568The smallest positive integer that does not appear twice in the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000929The constant term of the character polynomial of an integer partition. St000944The 3-degree of an integer partition. St000387The matching number of a graph. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000456The monochromatic index of a connected graph. St001545The second Elser number of a connected graph.