An improved upper bound for the multicolour Ramsey number of odd cycles
Abstract:
We show that the k-colour Ramsey number of an odd cycle of length 2ℓ+ 1 is at most (4ℓ)$^𝑘$ ⋅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.
| Zugehörige Institution(en) am KIT | Institut für Algebra und Geometrie (IAG) |
| Publikationstyp | Zeitschriftenaufsatz |
| Publikationsmonat/-jahr | 07.2026 |
| Sprache | Englisch |
| Identifikator | ISSN: 0095-8956 KITopen-ID: 1000199098 |
| Erschienen in | Journal of Combinatorial Theory, Series B |
| Verlag | Academic Press |
| Band | 179 |
| Seiten | 293–298 |
| Vorab online veröffentlicht am | 28.04.2026 |
| Schlagwörter | Ramsey theory; Odd cycles; Edge colourings; Chromatic number |
| Nachgewiesen in | Scopus Web of Science OpenAlex |