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

Journal of Combinatorial Theory Series B 2026 Open access

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Authors: Maria Axenovich, Wouter Cames van Batenburg, Oliver Janzer, Lukas Michel, Mathieu Rundström
DOI: 10.1016/j.jctb.2026.04.005
Cited by: 0

Abstract

We show that the k -colour Ramsey number of an odd cycle of length 2 ℓ + 1 is at most ( 4 ℓ ) k ⋅ k k / ℓ . 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.

Fields of Study & Subjects

Limits and Structures in Graph Theory Advanced Topology and Set Theory Computability Logic AI Algorithms

Publication details

Journal / source
Journal of Combinatorial Theory Series B
Volume
179
Pages
293–298
Publication date
28 April 2026
Language
EN