Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs
Combinatorics
2025-03-11 v2
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.
Keywords
Cite
@article{arxiv.1907.08029,
title = {Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs},
author = {Adam Kabela and Zdeněk Ryjáček and Petr Vrána},
journal= {arXiv preprint arXiv:1907.08029},
year = {2025}
}