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arXiv · 2510.25734

Ramsey Numbers in Kneser Graphs

Emily Heath·Grace McCourt·Alex Parker·Coy Schwieder·Shira Zerbib
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Abstract

We define the $r\textit{-Kneser Ramsey number}$ $R^{\textrm{KG}}_{r}(s, t)$ as the minimum integer $n$ such that every red/blue edge-coloring of the Kneser graph $\textrm{KG}(n,r)$ contains a red $s$-clique or a blue $t$-clique. We obtain general bounds on the numbers $R^{\textrm{KG}}_{r}(s, t)$, and make progress on two related Ramsey-type problems, one raised by Holmsen, Hrusak, and Roldán-Pensado, and the other posted by Pálvölgyi.

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Emily Heath, Grace McCourt, Alex Parker, Coy Schwieder, Shira Zerbib. 2025-11-10. Ramsey Numbers in Kneser Graphs. https://arxiv.org/abs/2510.25734

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