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^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	69
Journal	Bulletin of the Iranian Mathematical Society
Volume	50
Issue number	5
DOIs	https://doi.org/10.1007/s41980-024-00909-5
State	Published - Oct 2024

Keywords

05C35
05C38
05C40
Chord in a cycle
Longest cycle
Longest path
k-connected graph

Access to Document

10.1007/s41980-024-00909-5

Cite this

@article{0ff5137700524b0291f777dba2326a4c,

title = "A Conjecture Generalizing Thomassen{\textquoteright}s Chord Conjecture in Graph Theory",

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.",

keywords = "05C35, 05C38, 05C40, Chord in a cycle, Longest cycle, Longest path, k-connected graph",

author = "Xingzhi Zhan",

note = "Publisher Copyright: {\textcopyright} The Author(s) under exclusive licence to Iranian Mathematical Society 2024.",

year = "2024",

month = oct,

doi = "10.1007/s41980-024-00909-5",

language = "英语",

volume = "50",

journal = "Bulletin of the Iranian Mathematical Society",

issn = "1018-6301",

publisher = "Iranian Mathematical Society",

number = "5",

}

TY - JOUR

T1 - A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory

AU - Zhan, Xingzhi

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Iranian Mathematical Society 2024.

PY - 2024/10

Y1 - 2024/10

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.

KW - 05C35

KW - 05C38

KW - 05C40

KW - Chord in a cycle

KW - Longest cycle

KW - Longest path

KW - k-connected graph

UR - https://www.scopus.com/pages/publications/85201542133

U2 - 10.1007/s41980-024-00909-5

DO - 10.1007/s41980-024-00909-5

M3 - 文章

AN - SCOPUS:85201542133

SN - 1018-6301

VL - 50

JO - Bulletin of the Iranian Mathematical Society

JF - Bulletin of the Iranian Mathematical Society

IS - 5

M1 - 69

ER -

A Conjecture Generalizing Thomassen’s Chord Conjecture in Graph Theory

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this