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Identifier
Values
=>
Cc0020;cc-rep
([],1)=>1 ([],2)=>1 ([(0,1)],2)=>2 ([],3)=>1 ([(1,2)],3)=>2 ([(0,2),(1,2)],3)=>2 ([(0,1),(0,2),(1,2)],3)=>3 ([],4)=>1 ([(2,3)],4)=>2 ([(1,3),(2,3)],4)=>2 ([(0,3),(1,3),(2,3)],4)=>2 ([(0,3),(1,2)],4)=>2 ([(0,3),(1,2),(2,3)],4)=>2 ([(1,2),(1,3),(2,3)],4)=>3 ([(0,3),(1,2),(1,3),(2,3)],4)=>3 ([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>4 ([],5)=>1 ([(3,4)],5)=>2 ([(2,4),(3,4)],5)=>2 ([(1,4),(2,4),(3,4)],5)=>2 ([(0,4),(1,4),(2,4),(3,4)],5)=>2 ([(1,4),(2,3)],5)=>2 ([(1,4),(2,3),(3,4)],5)=>2 ([(0,1),(2,4),(3,4)],5)=>2 ([(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,4),(2,3),(3,4)],5)=>2 ([(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>3 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,3),(2,3),(2,4)],5)=>2 ([(0,1),(2,3),(2,4),(3,4)],5)=>3 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>3 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>3 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>3 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>3 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>3 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>4 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>4 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5 ([],6)=>1 ([(4,5)],6)=>2 ([(3,5),(4,5)],6)=>2 ([(2,5),(3,5),(4,5)],6)=>2 ([(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>2 ([(2,5),(3,4)],6)=>2 ([(2,5),(3,4),(4,5)],6)=>2 ([(1,2),(3,5),(4,5)],6)=>2 ([(3,4),(3,5),(4,5)],6)=>3 ([(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(0,1),(2,5),(3,5),(4,5)],6)=>2 ([(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,5),(2,4),(3,4)],6)=>2 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>2 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>3 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,3)],6)=>2 ([(1,5),(2,4),(3,4),(3,5)],6)=>2 ([(0,1),(2,5),(3,4),(4,5)],6)=>2 ([(1,2),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>2 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>3 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>3 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>3 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>2 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>3 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>3 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>3 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>3 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>3 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>3 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>3 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>3 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>4 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(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)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>3 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>3 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>3 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>4 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>4 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(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)=>4 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(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)=>5 ([(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)=>5 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(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)=>5 ([(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)=>4 ([(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)=>5 ([(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)=>5 ([(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)=>6
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Description
The Hadwiger number of the graph.
Also known as clique contraction number, this is the size of the largest complete minor.
References
[1] wikipedia:Hadwiger number
Code
def statistic(G):
    min_bound = G.chromatic_number()
    if G.is_planar():
        max_bound = 4
    else:
        max_bound = G.num_verts()
    for k in range(min_bound, max_bound+1):
        try:
            G.minor(graphs.CompleteGraph(k))
        except ValueError:
            return k-1
    return max_bound
Created
May 23, 2017 at 22:08 by Martin Rubey
Updated
May 24, 2017 at 08:46 by Martin Rubey