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arXiv · 2409.05931

Infinitely many minimally non-Ramsey size-linear graphs

Yuval Wigderson
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Abstract

A graph $G$ is said to be Ramsey size-linear if $r(G,H) =O_G (e(H))$ for every graph $H$ with no isolated vertices. Erdős, Faudree, Rousseau, and Schelp observed that $K_4$ is not Ramsey size-linear, but each of its proper subgraphs is, and they asked whether there exist infinitely many such graphs. In this short note, we answer this question in the affirmative.

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Yuval Wigderson. 2025-05-05. Infinitely many minimally non-Ramsey size-linear graphs. https://arxiv.org/abs/2409.05931

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