2024/02/07 by Xingzhi Zhan, Zhan, Xingzhi
Computer Science · Mathematics · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2402.04572
Thomassen's chord conjecture from 1976 states that every longest cycle in a 3-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 k-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.