Infinitely many minimally non-Ramsey size-linear graphs

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2025-05-10 DOI:10.1016/j.ejc.2025.104175

Yuval Wigderson

引用次数: 0

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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无穷多个最小非拉姆齐大小线性图

对于没有孤立顶点的每个图H，如果r(G，H)=OG(e(H))，则图G是拉姆齐大小线性的。Erdős, Faudree， Rousseau和Schelp观察到K4不是拉姆齐大小线性的，但它的每个适当子图都是线性的，他们问是否存在无限多个这样的图。在这篇短文中，我们肯定地回答了这个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.