Identifier
Identifier
Values
([],1) generating graphics... => 2
([],2) generating graphics... => 4
([(0,1)],2) generating graphics... => 3
([],3) generating graphics... => 6
([(1,2)],3) generating graphics... => 5
([(0,2),(1,2)],3) generating graphics... => 5
([(0,1),(0,2),(1,2)],3) generating graphics... => 4
([],4) generating graphics... => 8
([(2,3)],4) generating graphics... => 7
([(1,3),(2,3)],4) generating graphics... => 7
([(1,2),(1,3),(2,3)],4) generating graphics... => 6
([(0,3),(1,3),(2,3)],4) generating graphics... => 7
([(0,3),(1,2)],4) generating graphics... => 6
([(0,3),(1,2),(2,3)],4) generating graphics... => 7
([(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 6
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 8
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 6
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 5
([],5) generating graphics... => 10
([(3,4)],5) generating graphics... => 9
([(2,4),(3,4)],5) generating graphics... => 9
([(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(1,4),(2,4),(3,4)],5) generating graphics... => 9
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 9
([(1,4),(2,3)],5) generating graphics... => 8
([(1,4),(2,3),(3,4)],5) generating graphics... => 9
([(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 10
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,1),(2,4),(3,4)],5) generating graphics... => 8
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 9
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 9
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 10
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 11
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 11
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) generating graphics... => 9
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,1),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 8
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 8
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 7
([],6) generating graphics... => 12
([(4,5)],6) generating graphics... => 11
([(3,5),(4,5)],6) generating graphics... => 11
([(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(2,5),(3,4)],6) generating graphics... => 10
([(2,5),(3,4),(4,5)],6) generating graphics... => 11
([(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(1,2),(3,5),(4,5)],6) generating graphics... => 10
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 11
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 11
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 12
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 13
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 13
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(1,2),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 9
([(0,1),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 11
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 10
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 11
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 11
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 13
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 14
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) generating graphics... => 9
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 10
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) generating graphics... => 8
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) generating graphics... => 9
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,5),(1,4),(2,3)],6) generating graphics... => 9
([(0,1),(2,5),(3,4),(4,5)],6) generating graphics... => 10
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 9
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 11
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 13
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 11
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 10
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 13
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 15
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 12
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 10
([(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) generating graphics... => 8
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 10
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) generating graphics... => 10
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 13
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 10
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) generating graphics... => 13
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 11
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 12
([(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) generating graphics... => 9
([(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) generating graphics... => 14
([(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) generating graphics... => 10
([(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) generating graphics... => 8
([(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) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 14
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 15
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 12
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(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) generating graphics... => 10
([(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) generating graphics... => 8
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 12
([(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) generating graphics... => 9
click to show generating function       
Description
The number of facets of the stable set polytope of a graph.
The stable set polytope of a graph $G$ is the convex hull of the characteristic vectors of stable (or independent) sets of vertices of $G$ inside $\mathbb{R}^{V(G)}$.
Code
def stable_set_polytope(G):
    V = G.vertices()
    Vpos = { v:i for i,v in enumerate(V) }
    poly_vertices = []
    for S in Subsets(V):
        if G.is_independent_set(S):
            vert = [0]*len(V)
            for s in S:
                vert[Vpos[s]] = 1
            poly_vertices.append(vert)
    return Polyhedron(vertices=poly_vertices)

def statistic(G):
    return stable_set_polytope(G).n_facets()
Created
Nov 26, 2015 at 12:26 by Christian Stump
Updated
Nov 26, 2015 at 12:26 by Christian Stump