无限多最小拉姆齐大小线性图

arXiv - MATH - Combinatorics Pub Date : 2024-09-09 DOI:arxiv-2409.05931

Yuval Wigderson

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引用次数: 0

摘要

如果 $r(G,H)=O_G (e(H))$是一个没有孤立顶点的永久图 $H$，那么这个图 $G$就被称为拉姆齐大小线性图。Erd\H{o}s、Faudree、Rousseau 和Schelp 发现 $K_4$ 不是拉姆齐大小线性图，但它的每个预子图都是，他们问是否存在无限多这样的图。

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Infinitely many minimally Ramsey size-linear graphs

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. Erd\H{o}s, 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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arXiv - MATH - Combinatorics

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