Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001570
Mapping
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001570: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,4,3,2] => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[4,3,2,1] => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,2,5,4,3] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,3,2,5,4] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[1,3,5,4,2] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,4,2,5,3] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[1,4,3,2,5] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[1,4,3,5,2] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[1,4,5,3,2] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,5,2,4,3] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,5,3,2,4] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[1,5,3,4,2] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,5,4,2,3] => [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,5,4,3,2] => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
[2,1,5,4,3] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[2,5,4,3,1] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[3,1,5,4,2] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[3,2,1,5,4] => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[3,2,5,4,1] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[3,5,4,2,1] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[4,1,5,3,2] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[4,2,1,5,3] => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[4,2,5,3,1] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[4,3,1,5,2] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[4,3,2,1,5] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[4,3,2,5,1] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[4,3,5,2,1] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[4,5,3,2,1] => [3,1,1] => [1,2] => ([(1,2)],3)
 => 2
[5,1,4,3,2] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[5,2,1,4,3] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[5,2,4,3,1] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[5,3,1,4,2] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[5,3,2,1,4] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[5,3,2,4,1] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[5,3,4,2,1] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[5,4,1,3,2] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[5,4,2,1,3] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[5,4,2,3,1] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[5,4,3,1,2] => [1,2,2] => [1,2] => ([(1,2)],3)
 => 2
[5,4,3,2,1] => [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 2
[1,2,3,6,5,4] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,2,4,3,6,5] => [2,2,2] => [3] => ([],3)
 => 3
[1,2,4,6,5,3] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,2,5,3,6,4] => [2,2,2] => [3] => ([],3)
 => 3
[1,2,5,4,3,6] => [2,2,2] => [3] => ([],3)
 => 3
[1,2,5,4,6,3] => [2,2,2] => [3] => ([],3)
 => 3
[1,2,5,6,4,3] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,2,6,3,5,4] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,2,6,4,3,5] => [2,2,2] => [3] => ([],3)
 => 3
[1,2,6,4,5,3] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
Description
The minimal number of edges to add to make a graph Hamiltonian. A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.