English

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 33-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 kk-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}
}