On Vizing's problem for triangle-free graphs
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914020688134144 |
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| author | Kang, Ross J. Rosenfeld, Matthieu |
| author_facet | Kang, Ross J. Rosenfeld, Matthieu |
| contents | We prove that $χ(G) \le \lceil (Δ+1)/2\rceil+1$ for any triangle-free graph $G$ of maximum degree $Δ$ provided $Δ\ge 524$. This gives tangible progress towards an old problem of Vizing, in a form cast by Reed. We use a method of Hurley and Pirot, which in turn relies on a new counting argument of the second author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10876 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Vizing's problem for triangle-free graphs Kang, Ross J. Rosenfeld, Matthieu Combinatorics 05C15, 05C35 We prove that $χ(G) \le \lceil (Δ+1)/2\rceil+1$ for any triangle-free graph $G$ of maximum degree $Δ$ provided $Δ\ge 524$. This gives tangible progress towards an old problem of Vizing, in a form cast by Reed. We use a method of Hurley and Pirot, which in turn relies on a new counting argument of the second author. |
| title | On Vizing's problem for triangle-free graphs |
| topic | Combinatorics 05C15, 05C35 |
| url | https://arxiv.org/abs/2309.10876 |