支点小调和Erdős-Hajnal猜想

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-04-16 DOI:10.1016/j.jctb.2025.04.004

James Davies

引用次数: 0

摘要

证明了Kim和Oum的一个猜想，即图的每一个适当的支点-次闭类都具有强Erdős-Hajnal性质。更准确地说，对于每个图H，存在ϵ>；0，使得每个n顶点图与H没有轴心次同构包含两个顶点集A，B，使得|A|，|B|小于ϵn和A对于B是完全的或反完全的。

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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Pivot-minors and the Erdős-Hajnal conjecture

We prove a conjecture of Kim and Oum that every proper pivot-minor-closed class of graphs has the strong Erdős-Hajnal property. More precisely, for every graph H, there exists

ϵ > 0

such that every n-vertex graph with no pivot-minor isomorphic to H contains two sets

A, B

of vertices such that

| A |, | B | ⩾ ϵ n

and A is complete or anticomplete to B.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.