An improved upper bound for the multicolour Ramsey number of odd cycles

Fuente: arXiv
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Auteurs principaux: Axenovich, Maria, van Batenburg, Wouter Cames, Janzer, Oliver, Michel, Lukas, Rundström, Mathieu
Format: Preprint
Publié: 2025
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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