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arXiv · 2511.16656

The multicolour size Ramsey number of a path

Csongor Beke·Anqi Li·Julian Sahasrabudhe
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Abstract

In this paper, we determine the $r$-colour size Ramsey number of the path $P_k$, up to constants. In particular, for every fixed $r \geq 2$ and $k \geq 100\log r$, we have \[ \widehat{R}_r(P_k)=Θ((r^2 \log r) \, k).\] Perhaps surprisingly, we do this by improving the lower bound on $\widehat{R}_r(P_k)$.

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Csongor Beke, Anqi Li, Julian Sahasrabudhe. 2026-04-16. The multicolour size Ramsey number of a path. https://arxiv.org/abs/2511.16656

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