Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs

2019/07/18 by Kabela, Adam, Ryjáček, Zdeněk, Vrána, Petr
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.08029

Abstract

We continue studying Thomassen's conjecture (every 4-connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2-connected claw-free graph has a Tutte cycle), and we extend the equivalent formulation as follows: In each connected claw-free graph, every two vertices are connected by a maximal path which is a Tutte path.

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