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Identifier
Values
=>
Cc0020;cc-rep
([],0)=>0 ([],1)=>0 ([],2)=>0 ([(0,1)],2)=>1 ([],3)=>0 ([(1,2)],3)=>1 ([(0,2),(1,2)],3)=>2 ([(0,1),(0,2),(1,2)],3)=>3 ([],4)=>0 ([(2,3)],4)=>1 ([(1,3),(2,3)],4)=>2 ([(0,3),(1,3),(2,3)],4)=>2 ([(0,3),(1,2)],4)=>1 ([(0,3),(1,2),(2,3)],4)=>3 ([(1,2),(1,3),(2,3)],4)=>3 ([(0,3),(1,2),(1,3),(2,3)],4)=>4 ([(0,2),(0,3),(1,2),(1,3)],4)=>4 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>5 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>5 ([],5)=>0 ([(3,4)],5)=>1 ([(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)=>1 ([(1,4),(2,3),(3,4)],5)=>3 ([(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)=>3 ([(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>5 ([(1,3),(1,4),(2,3),(2,4)],5)=>4 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>5 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>4 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>6 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7 ([(0,4),(1,3),(2,3),(2,4)],5)=>4 ([(0,1),(2,3),(2,4),(3,4)],5)=>3 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>5 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>5 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>7 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>5 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>8 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>6 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>7 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>9 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>10 ([],6)=>0 ([(4,5)],6)=>1 ([(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)=>1 ([(2,5),(3,4),(4,5)],6)=>3 ([(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)=>3 ([(0,1),(2,5),(3,5),(4,5)],6)=>2 ([(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>3 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,5),(1,5),(2,4),(3,4)],6)=>2 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>4 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>3 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>6 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>8 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,4),(2,3)],6)=>1 ([(1,5),(2,4),(3,4),(3,5)],6)=>4 ([(0,1),(2,5),(3,4),(4,5)],6)=>3 ([(1,2),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>4 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>5 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>6 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>6 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>7 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>5 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>5 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>6 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>5 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(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)=>6 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>6 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>5 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>7 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>7 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>6 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>8 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>8 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,4),(1,5),(2,3),(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)],6)=>7 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>9 ([(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)=>6 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>7 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>7 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>7 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>6 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>7 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>6 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>7 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>7 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>8 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>8 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(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)=>9 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>7 ([(0,1),(0,2),(0,3),(1,4),(1,5),(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)],6)=>10 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>10 ([(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)=>10 ([(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)=>6 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>7 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>8 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7 ([(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)=>7 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>8 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>8 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(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)=>9 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>9 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>7 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>8 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>8 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>7 ([(0,1),(0,3),(0,5),(1,2),(1,4),(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),(3,4),(3,5),(4,5)],6)=>10 ([(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)=>11 ([(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)=>10 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>10 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(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)=>12 ([(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)=>12 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>11 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>11 ([(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)=>12 ([(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)=>12 ([(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)=>13 ([(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)=>13 ([(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)=>13
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Description
The length of a longest trail in a graph.
A trail is a sequence of distinct edges, such that two consecutive edges share a vertex.
References
[1] wikipedia:Path_(graph_theory)
Code
def statistic(G):
    def children(p):
        A = p[0][0]
        for u in G[A]:
            if (u, A) not in p and (A, u) not in p:
                yield ((u, A),) + p

        B = p[-1][1]
        for u in G[B]:
            if (u, B) not in p and (B, u) not in p:
                yield p + ((B, u),)
    if not G.edges():
        return 0
    trails = RecursivelyEnumeratedSet([(e,) for e in G.edges(labels=False)],
                                      children)
    return max(len(p) for p in trails)
Created
Nov 28, 2020 at 22:48 by Martin Rubey
Updated
Nov 28, 2020 at 22:48 by Martin Rubey