Identifier
Values
=>
Cc0020;cc-rep
([],1)=>2 ([],2)=>4 ([(0,1)],2)=>3 ([],3)=>6 ([(1,2)],3)=>5 ([(0,2),(1,2)],3)=>5 ([(0,1),(0,2),(1,2)],3)=>4 ([],4)=>8 ([(2,3)],4)=>7 ([(1,3),(2,3)],4)=>7 ([(0,3),(1,3),(2,3)],4)=>7 ([(0,3),(1,2)],4)=>6 ([(0,3),(1,2),(2,3)],4)=>7 ([(1,2),(1,3),(2,3)],4)=>6 ([(0,3),(1,2),(1,3),(2,3)],4)=>6 ([(0,2),(0,3),(1,2),(1,3)],4)=>8 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>6 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>5 ([],5)=>10 ([(3,4)],5)=>9 ([(2,4),(3,4)],5)=>9 ([(1,4),(2,4),(3,4)],5)=>9 ([(0,4),(1,4),(2,4),(3,4)],5)=>9 ([(1,4),(2,3)],5)=>8 ([(1,4),(2,3),(3,4)],5)=>9 ([(0,1),(2,4),(3,4)],5)=>8 ([(2,3),(2,4),(3,4)],5)=>8 ([(0,4),(1,4),(2,3),(3,4)],5)=>9 ([(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(1,3),(1,4),(2,3),(2,4)],5)=>10 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>10 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>8 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>11 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(0,4),(1,3),(2,3),(2,4)],5)=>9 ([(0,1),(2,3),(2,4),(3,4)],5)=>7 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>8 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>7 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>11 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>9 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>8 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>9 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>9 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6 ([],6)=>12 ([(4,5)],6)=>11 ([(3,5),(4,5)],6)=>11 ([(2,5),(3,5),(4,5)],6)=>11 ([(1,5),(2,5),(3,5),(4,5)],6)=>11 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>11 ([(2,5),(3,4)],6)=>10 ([(2,5),(3,4),(4,5)],6)=>11 ([(1,2),(3,5),(4,5)],6)=>10 ([(3,4),(3,5),(4,5)],6)=>10 ([(1,5),(2,5),(3,4),(4,5)],6)=>11 ([(0,1),(2,5),(3,5),(4,5)],6)=>10 ([(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>11 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,5),(1,5),(2,4),(3,4)],6)=>10 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>12 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>11 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>11 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>12 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>13 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>13 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>14 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(2,3)],6)=>9 ([(1,5),(2,4),(3,4),(3,5)],6)=>11 ([(0,1),(2,5),(3,4),(4,5)],6)=>10 ([(1,2),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>11 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>10 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>10 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>9 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>9 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>13 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>12 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>11 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>13 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>11 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>11 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>9 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>12 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>10 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>10 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>11 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>10 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>15 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>12 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>13 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>11 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>11 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>12 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>13 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>11 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>12 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>10 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>14 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>15 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>12 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>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)=>9 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>8 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>10 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>9 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>9 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>10 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>10 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>10 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>13 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>12 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>12 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>11 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>11 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(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)=>9 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(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)=>8 ([(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)=>8 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>12 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>10 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>10 ([(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)=>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)=>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)=>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)=>7
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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