Processing math: 100%

Your data matches 89 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000667
(load all 2 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000667: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [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)
 => [4,1]
 => [1]
 => 1
([(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [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)
 => [5,1]
 => [1]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [1]
 => 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)
 => [5,1]
 => [1]
 => 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)
 => [5,1]
 => [1]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 2
Description
The greatest common divisor of the parts of the partition.
Matching statistic: St000993
(load all 2 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => 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)
 => [4,1]
 => [2,1,1,1]
 => 1
([(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [3,3]
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2,2,1,1]
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [3,2,1]
 => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2,2,1,1]
 => 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)
 => [5,1]
 => [2,1,1,1,1]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 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)
 => [5,1]
 => [2,1,1,1,1]
 => 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)
 => [5,1]
 => [2,1,1,1,1]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => 2
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => [14,1]
 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => ? = 1
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St001038
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001038: Dyck paths ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 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)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => 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)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 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)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 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)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => [9,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => [14,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1
Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
Matching statistic: St001816
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St001816: Standard tableaux ⟶ ℤResult quality: 75% ●values known / values provided: 95%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [[1,2,5],[3,4]]
 => 1 = 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)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 0 = 1 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [[1,3,6],[2,5],[4]]
 => 0 = 1 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => 1 = 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)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 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)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 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)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [[1,2,5],[3,4]]
 => 1 = 2 - 1
([(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)
 => [7,1]
 => [[1,3,4,5,6,7,8],[2]]
 => ? = 1 - 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,7),(1,6),(2,5),(3,4)],8)
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => ? = 2 - 1
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => [9,1]
 => [[1,3,4,5,6,7,8,9,10],[2]]
 => ? = 1 - 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => [14,1]
 => [[1,3,4,5,6,7,8,9,10,11,12,13,14,15],[2]]
 => ? = 1 - 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [4,2,2]
 => [[1,2,7,8],[3,4],[5,6]]
 => ? = 2 - 1
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => ? = 2 - 1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => ? = 4 - 1
Description
Eigenvalues of the top-to-random operator acting on a simple module. These eigenvalues are given in [1] and [3]. The simple module of the symmetric group indexed by a partition λ has dimension equal to the number of standard tableaux of shape λ. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape λ; this statistic gives all the eigenvalues of the operator acting on the module. This statistic bears different names, such as the type in [2] or eig in [3]. Similarly, the eigenvalues of the random-to-random operator acting on a simple module is [[St000508]].
Matching statistic: St001119
(load all 16 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
St001119: Graphs ⟶ ℤResult quality: 75% ●values known / values provided: 95%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 0 = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 1 = 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)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => 0 = 1 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => 0 = 1 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 0 = 1 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => 0 = 1 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => 1 = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => 0 = 1 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 0 = 1 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 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)
 => 0 = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 0 = 1 - 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)
 => 0 = 1 - 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)
 => 0 = 1 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 1 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 1
([(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)
 => ? = 1 - 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,7),(1,6),(2,5),(3,4)],8)
 => ? = 2 - 1
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ? = 2 - 1
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ? = 1 - 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ? = 1 - 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ? = 4 - 1
Description
The length of a shortest maximal path in a graph.
Matching statistic: St000093
(load all 3 compositions to match this statistic)
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
St000093: Graphs ⟶ ℤResult quality: 75% ●values known / values provided: 88%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(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)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(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)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,4)],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),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(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),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(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)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => 2
([(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)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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
([(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),(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
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10)],12)
 => ? = 2
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,3),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,7),(2,8),(2,9),(3,4),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8)],10)
 => ? = 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,5),(2,6),(2,7),(2,8),(3,4),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,7),(0,8),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,6),(1,8),(1,11),(2,3),(2,5),(2,8),(2,10),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,10),(6,7),(6,11),(7,8),(9,10),(9,11),(10,11)],12)
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,8),(1,9),(2,3),(2,4),(2,7),(2,9),(3,4),(3,6),(3,9),(4,5),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],10)
 => ? = 2
([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,1),(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ? = 2
([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ? = 2
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(0,3),(0,8),(0,9),(1,2),(1,7),(1,9),(2,5),(2,7),(2,9),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
 => ?
 => ? = 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(0,3),(0,9),(0,13),(0,14),(1,2),(1,8),(1,12),(1,14),(2,6),(2,8),(2,12),(2,14),(3,7),(3,9),(3,13),(3,14),(4,6),(4,8),(4,10),(4,11),(4,12),(4,13),(4,14),(5,7),(5,9),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,10),(6,12),(6,13),(6,14),(7,9),(7,10),(7,12),(7,13),(7,14),(8,11),(8,12),(8,14),(9,11),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,14),(13,14)],15)
 => ?
 => ? = 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ? = 2
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
 => ?
 => ? = 4
Description
The cardinality of a maximal independent set of vertices of a graph. An independent set of a graph is a set of pairwise non-adjacent vertices. A maximum independent set is an independent set of maximum cardinality. This statistic is also called the independence number or stability number α(G) of G.
Matching statistic: St000097
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000097: Graphs ⟶ ℤResult quality: 75% ●values known / values provided: 86%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(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)
 => ([],3)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(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)
 => ([],3)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,5),(3,4)],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),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(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),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(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)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ([(0,7),(1,6),(2,5),(3,4)],8)
 => 2
([(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)
 => ([],4)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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)
 => ([(2,5),(3,4)],6)
 => 2
([(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),(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
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(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)],6)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(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)
 => 2
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10)],12)
 => ?
 => ? = 2
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,3),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,7),(2,8),(2,9),(3,4),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8)],10)
 => ?
 => ? = 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,5),(2,6),(2,7),(2,8),(3,4),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ([],9)
 => ? = 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(2,7),(3,7),(4,6),(5,6)],8)
 => ? = 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,7),(0,8),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,6),(1,8),(1,11),(2,3),(2,5),(2,8),(2,10),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,10),(6,7),(6,11),(7,8),(9,10),(9,11),(10,11)],12)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,8),(1,9),(2,3),(2,4),(2,7),(2,9),(3,4),(3,6),(3,9),(4,5),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],10)
 => ?
 => ? = 2
([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,1),(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ?
 => ? = 2
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ?
 => ? = 2
([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ?
 => ? = 2
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 3
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(0,3),(0,8),(0,9),(1,2),(1,7),(1,9),(2,5),(2,7),(2,9),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
 => ?
 => ?
 => ? = 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(0,3),(0,9),(0,13),(0,14),(1,2),(1,8),(1,12),(1,14),(2,6),(2,8),(2,12),(2,14),(3,7),(3,9),(3,13),(3,14),(4,6),(4,8),(4,10),(4,11),(4,12),(4,13),(4,14),(5,7),(5,9),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,10),(6,12),(6,13),(6,14),(7,9),(7,10),(7,12),(7,13),(7,14),(8,11),(8,12),(8,14),(9,11),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,14),(13,14)],15)
 => ?
 => ?
 => ? = 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ?
 => ? = 2
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
 => ?
 => ?
 => ? = 4
Description
The order of the largest clique of the graph. A clique in a graph G is a subset U⊆V(G) such that any pair of vertices in U are adjacent. I.e. the subgraph induced by U is a complete graph.
Matching statistic: St000786
(load all 3 compositions to match this statistic)
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
St000786: Graphs ⟶ ℤResult quality: 75% ●values known / values provided: 85%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(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)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(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)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,4)],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),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(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),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(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)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 2
([(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)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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
([(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),(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
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(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)
 => 2
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 2
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 2
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10)],12)
 => ? = 2
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,3),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,7),(2,8),(2,9),(3,4),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8)],10)
 => ? = 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,5),(2,6),(2,7),(2,8),(3,4),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,7),(0,8),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,6),(1,8),(1,11),(2,3),(2,5),(2,8),(2,10),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,10),(6,7),(6,11),(7,8),(9,10),(9,11),(10,11)],12)
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,8),(1,9),(2,3),(2,4),(2,7),(2,9),(3,4),(3,6),(3,9),(4,5),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],10)
 => ? = 2
([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,1),(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ? = 2
([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ? = 2
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 3
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(0,3),(0,8),(0,9),(1,2),(1,7),(1,9),(2,5),(2,7),(2,9),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
 => ?
 => ? = 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(0,3),(0,9),(0,13),(0,14),(1,2),(1,8),(1,12),(1,14),(2,6),(2,8),(2,12),(2,14),(3,7),(3,9),(3,13),(3,14),(4,6),(4,8),(4,10),(4,11),(4,12),(4,13),(4,14),(5,7),(5,9),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,10),(6,12),(6,13),(6,14),(7,9),(7,10),(7,12),(7,13),(7,14),(8,11),(8,12),(8,14),(9,11),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,14),(13,14)],15)
 => ?
 => ? = 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ? = 2
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
 => ?
 => ? = 4
Description
The maximal number of occurrences of a colour in a proper colouring of a graph. To any proper colouring with the minimal number of colours possible we associate the integer partition recording how often each colour is used. This statistic records the largest part occurring in any of these partitions. For example, the graph on six vertices consisting of a square together with two attached triangles - ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) in the list of values - is three-colourable and admits two colouring schemes, [2,2,2] and [3,2,1]. Therefore, the statistic on this graph is 3.
Matching statistic: St000098
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000098: Graphs ⟶ ℤResult quality: 75% ●values known / values provided: 85%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(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)
 => ([],3)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(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)
 => ([],3)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,5),(3,4)],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),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(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),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(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)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ([(0,7),(1,6),(2,5),(3,4)],8)
 => 2
([(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)
 => ([],4)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(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)
 => ([(2,5),(3,4)],6)
 => 2
([(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),(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
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(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)],6)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(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),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(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)
 => 2
([(1,6),(2,5),(3,4)],7)
 => ([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([],8)
 => ? = 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10)],12)
 => ?
 => ? = 2
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,3),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,7),(2,8),(2,9),(3,4),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8)],10)
 => ?
 => ? = 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,5),(2,6),(2,7),(2,8),(3,4),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ([],9)
 => ? = 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(2,7),(3,7),(4,6),(5,6)],8)
 => ? = 2
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([],8)
 => ? = 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,7),(0,8),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ?
 => ? = 3
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([],8)
 => ? = 1
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,6),(1,8),(1,11),(2,3),(2,5),(2,8),(2,10),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(4,9),(5,6),(5,7),(5,10),(6,7),(6,11),(7,8),(9,10),(9,11),(10,11)],12)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,8),(1,9),(2,3),(2,4),(2,7),(2,9),(3,4),(3,6),(3,9),(4,5),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],10)
 => ?
 => ? = 2
([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,1),(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ?
 => ? = 2
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ?
 => ? = 2
([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)
 => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ?
 => ? = 2
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
 => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ? = 3
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(0,3),(0,8),(0,9),(1,2),(1,7),(1,9),(2,5),(2,7),(2,9),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
 => ?
 => ?
 => ? = 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(0,3),(0,9),(0,13),(0,14),(1,2),(1,8),(1,12),(1,14),(2,6),(2,8),(2,12),(2,14),(3,7),(3,9),(3,13),(3,14),(4,6),(4,8),(4,10),(4,11),(4,12),(4,13),(4,14),(5,7),(5,9),(5,10),(5,11),(5,12),(5,13),(5,14),(6,8),(6,10),(6,12),(6,13),(6,14),(7,9),(7,10),(7,12),(7,13),(7,14),(8,11),(8,12),(8,14),(9,11),(9,13),(9,14),(10,11),(10,12),(10,13),(10,14),(11,12),(11,13),(11,14),(12,14),(13,14)],15)
 => ?
 => ?
 => ? = 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ?
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ?
 => ?
 => ? = 2
([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
 => ?
 => ?
 => ? = 2
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
 => ?
 => ?
 => ? = 4
Description
The chromatic number of a graph. The minimal number of colors needed to color the vertices of the graph such that no two vertices which share an edge have the same color.
Matching statistic: St001316
(load all 12 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
St001316: Graphs ⟶ ℤResult quality: 75% ●values known / values provided: 85%●distinct values known / distinct values provided: 75%
Values
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(2,3)],4)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(3,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(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)
 => ([(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)
 => 1
([(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(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)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 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)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 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)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(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)
 => ?
 => ? = 1
([(0,7),(1,6),(2,5),(3,4)],8)
 => ([(0,7),(1,6),(2,5),(3,4)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
 => ?
 => ? = 2
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ?
 => ? = 1
([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ?
 => ? = 1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 2
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
 => ?
 => ? = 4
Description
The domatic number of a graph. This is the maximal size of a partition of the vertices into dominating sets.
The following 79 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000259The diameter of a connected graph. St001674The number of vertices of the largest induced star graph in the graph. St001029The size of the core of a graph. St001494The Alon-Tarsi number of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001642The Prague dimension of a graph. St001271The competition number of a graph. St000260The radius of a connected graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000310The minimal degree of a vertex of a graph. St001330The hat guessing number of a graph. St000264The girth of a graph, which is not a tree. St000456The monochromatic index of a connected graph. St001592The maximal number of simple paths between any two different vertices of a graph. St000379The number of Hamiltonian cycles in a graph. St000455The second largest eigenvalue of a graph if it is integral. St001571The Cartan determinant of the integer partition. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St000284The Plancherel distribution on integer partitions. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St001568The smallest positive integer that does not appear twice in the partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000567The sum of the products of all pairs of parts. St000699The toughness times the least common multiple of 1,. St000929The constant term of the character polynomial of an integer partition. 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. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001657The number of twos in an integer partition. St001118The acyclic chromatic index of a graph. St001281The normalized isoperimetric number of a graph. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001339The irredundance number of a graph. St001765The number of connected components of the friends and strangers graph. St001322The size of a minimal independent dominating set in a graph. St001829The common independence number of a graph. St001651The Frankl number of a lattice. St000261The edge connectivity of a graph. St001613The binary logarithm of the size of the center of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001618The cardinality of the Frattini sublattice of a lattice. St001820The size of the image of the pop stack sorting operator. St001845The number of join irreducibles minus the rank of a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001703The villainy of a graph. St001877Number of indecomposable injective modules with projective dimension 2. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St001624The breadth of a lattice. St001625The Möbius invariant of a lattice. 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. St001626The number of maximal proper sublattices of a lattice. St001875The number of simple modules with projective dimension at most 1. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001754The number of tolerances of a finite lattice. St001060The distinguishing index of a graph.