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 $\mathbb{R}^{V(G)}$.
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
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