***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001649 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- 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) ----------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------- Created: Nov 28, 2020 at 22:48 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 28, 2020 at 22:48 by Martin Rubey