Work

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

Year: 2026

Type: article

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.

Source: Journal of Combinatorial Theory Series B

DOI: 10.1016/j.jctb.2026.04.005

Authors: Maria Axenovich, Wouter Cames van Batenburg, Oliver Janzer, Lukas Michel, Mathieu Rundström

Institutions: Karlsruhe Institute of Technology, Université Libre de Bruxelles, École Polytechnique Fédérale de Lausanne, University of Oxford, University of Waterloo

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funder: Fonds De La Recherche Scientifique - FNRS