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Statistic identifier: St000301
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Collection: Graphs
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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 $\mathbb{R}^{V(G)}$.
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References:
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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()
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Statistic values:
([],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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Created: Nov 26, 2015 at 12:26 by Christian Stump
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Last Updated: Nov 26, 2015 at 12:26 by Christian Stump