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arXiv · 2601.10238

Ramsey number of a cycle versus a graph of a given size

Stijn Cambie·Andrea Freschi·Patryk Morawski·Kalina Petrova·Alexey Pokrovskiy
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Abstract

In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R(C_k,H)$ is at most $2m+\lfloor \frac{k-1}{2} \rfloor$, provided $m$ is sufficiently large with respect to $k$. This settles a problem of Erdős, Faudree, Rousseau and Schelp.

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Stijn Cambie, Andrea Freschi, Patryk Morawski, Kalina Petrova, Alexey Pokrovskiy. 2026-01-15. Ramsey number of a cycle versus a graph of a given size. https://arxiv.org/abs/2601.10238

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