Ramsey Numbers in Kneser Graphs

Emily Heath; Grace McCourt; Alex Parker; Coy Schwieder; Shira Zerbib

Ramsey Numbers in Kneser Graphs

Combinatorics 2025-11-12 v2

Authors: Emily Heath , Grace McCourt , Alex Parker , Coy Schwieder , Shira Zerbib

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 Rold\'an-Pensado, and the other posted by P\'alv\"olgyi.

Keywords

ramsey numbers ramsey theory

Cite

@article{arxiv.2510.25734,
  title  = {Ramsey Numbers in Kneser Graphs},
  author = {Emily Heath and Grace McCourt and Alex Parker and Coy Schwieder and Shira Zerbib},
  journal= {arXiv preprint arXiv:2510.25734},
  year   = {2025}
}

Ramsey Numbers in Kneser Graphs

Abstract

Keywords

Cite

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