Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl
{"title":"Erdős–Hajnal for graphs with no 5‐hole","authors":"Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl","doi":"10.1112/plms.12504","DOIUrl":null,"url":null,"abstract":"Abstract The Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. We also prove several further results: for instance, that if is a cycle and is the complement of a forest, there exists such that every graph containing neither of as an induced subgraph has a clique or stable set of cardinality at least .","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":"35 1","pages":"0"},"PeriodicalIF":1.5000,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the London Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/plms.12504","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
Abstract The Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. We also prove several further results: for instance, that if is a cycle and is the complement of a forest, there exists such that every graph containing neither of as an induced subgraph has a clique or stable set of cardinality at least .
期刊介绍：
The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers.
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