A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory

Xingzhi Zhan

doi:10.1007/s41980-024-00909-5

A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory

Xingzhi Zhan^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
文章编号	69
期刊	Bulletin of the Iranian Mathematical Society
卷	50
期	5
DOI	https://doi.org/10.1007/s41980-024-00909-5
出版状态	已出版 - 10月 2024

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abstract = "Thomassen{\textquoteright}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{\textquoteright}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{\textquoteright}s conjecture.",

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N2 - 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.

AB - 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.

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KW - 05C38

KW - 05C40

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KW - Longest cycle

KW - Longest path

KW - k-connected graph

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JO - Bulletin of the Iranian Mathematical Society

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A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory

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