Induced Subgraphs of Induced Subgraphs of Large Chromatic Number

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2023-09-25 DOI:10.1007/s00493-023-00061-4

António Girão, Freddie Illingworth, Emil Powierski, Michael Savery, Alex Scott, Youri Tamitegama, Jane Tan

引用次数: 5

Abstract

We prove that, for every graph F with at least one edge, there is a constant \(c_F\) such that there are graphs of arbitrarily large chromatic number and the same clique number as F in which every F-free induced subgraph has chromatic number at most \(c_F\). This generalises recent theorems of Briański, Davies and Walczak, and Carbonero, Hompe, Moore and Spirkl. Our results imply that for every \(r\geqslant 3\) the class of \(K_r\)-free graphs has a very strong vertex Ramsey-type property, giving a vast generalisation of a result of Folkman from 1970. We also prove related results for tournaments, hypergraphs and infinite families of graphs, and show an analogous statement for graphs where clique number is replaced by odd girth.

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大色数诱导子图的诱导子图

我们证明，对于每个至少有一条边的图F，存在一个常数\（c_F\），使得存在具有任意大色数和与F相同团数的图，其中每个无F诱导子图最多有色数\（c_F \）。这推广了Briański，Davies和Walczak，以及Carbonero，Hompe，Moore和Spirkl最近的定理。我们的结果表明，对于每一个\（r\geqslant3\）类\（K_r\）-自由图都具有很强的顶点Ramsey型性质，给出了Folkman 1970年的一个结果的广泛推广。我们还证明了锦标赛、超图和无限图族的相关结果，并给出了团数被奇数围数取代的图的类似陈述。

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

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.