A conjecture implying Thomassen's chord conjecture in graph theory
Combinatorics
2024-02-08 v1
Abstract
Thomassen's chord conjecture from 1976 states that every longest cycle in a -connected graph has a chord. This is one of the most important unsolved problems in graph theory. We pose a new conjecture which implies Thomassen's conjecture. It involves bound vertices in a longest path between two vertices in a -connected graph. We also give supporting evidence and analyze a special case. The purpose of making this new conjecture is to explore the surroundings of Thomassen's conjecture.
Keywords
Cite
@article{arxiv.2402.04572,
title = {A conjecture implying Thomassen's chord conjecture in graph theory},
author = {Xingzhi Zhan},
journal= {arXiv preprint arXiv:2402.04572},
year = {2024}
}