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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St001649
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Collection: Graphs
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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)]]
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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)
-----------------------------------------------------------------------------
Statistic values:
([],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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Created: Nov 28, 2020 at 22:48 by Martin Rubey
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Last Updated: Nov 28, 2020 at 22:48 by Martin Rubey