An improved upper bound for the multicolour Ramsey number of odd cycles
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909860515282944 |
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| author | Axenovich, Maria van Batenburg, Wouter Cames Janzer, Oliver Michel, Lukas Rundström, Mathieu |
| author_facet | Axenovich, Maria van Batenburg, Wouter Cames Janzer, Oliver Michel, Lukas Rundström, Mathieu |
| contents | We show that the $k$-colour Ramsey number of an odd cycle of length $2 \ell + 1$ is at most $(4 \ell)^k \cdot k^{k/\ell}$. This proves a conjecture of Fox and is the first improvement in the exponent that goes beyond an absolute constant factor since the work of Bondy and Erdős from 1973. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved upper bound for the multicolour Ramsey number of odd cycles Axenovich, Maria van Batenburg, Wouter Cames Janzer, Oliver Michel, Lukas Rundström, Mathieu Combinatorics We show that the $k$-colour Ramsey number of an odd cycle of length $2 \ell + 1$ is at most $(4 \ell)^k \cdot k^{k/\ell}$. This proves a conjecture of Fox and is the first improvement in the exponent that goes beyond an absolute constant factor since the work of Bondy and Erdős from 1973. |
| title | An improved upper bound for the multicolour Ramsey number of odd cycles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.17981 |