A conjecture implying Thomassen's chord conjecture in graph theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914669974781952 |
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| author | Zhan, Xingzhi |
| author_facet | Zhan, Xingzhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A conjecture implying Thomassen's chord conjecture in graph theory Zhan, Xingzhi Combinatorics 05C38, 05C40, 05C35 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. |
| title | A conjecture implying Thomassen's chord conjecture in graph theory |
| topic | Combinatorics 05C38, 05C40, 05C35 |
| url | https://arxiv.org/abs/2402.04572 |