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arXiv · 2608.30481

The Multicolour Size--Ramsey Number of an Even Cycle

Lanchao Wang·Xiaolin Wang
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Abstract

We determine the $k$-colour size--Ramsey number of even cycles up to absolute constant factors. For every $k\ge2$ and every even $n\ge100\log k$, \[ \widehat R_k(C_n)=Θ(k^2\log k)n. \] The lower bound follows from the corresponding result of Beke, Li and Sahasrabudhe for paths, while our upper bound improves the previous best estimate $O(k^{34}n)$ of Javadi, Kohayakawa and Miralaei.

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Lanchao Wang, Xiaolin Wang. 2026-08-31. The Multicolour Size--Ramsey Number of an Even Cycle. https://arxiv.org/abs/2608.30481

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