{"title":"Some results and problems on tournament structure","authors":"Tung Nguyen , Alex Scott , Paul Seymour","doi":"10.1016/j.jctb.2025.02.002","DOIUrl":null,"url":null,"abstract":"<div><div>This paper is a survey of results and problems related to the following question: is it true that if <em>G</em> is a tournament with sufficiently large chromatic number, then <em>G</em> has two vertex-disjoint subtournaments <span><math><mi>A</mi><mo>,</mo><mi>B</mi></math></span>, both with large chromatic number, such that all edges between them are directed from <em>A</em> to <em>B</em>? We describe what we know about this question, and report some progress on several other related questions, on tournament colouring and domination.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"173 ","pages":"Pages 146-183"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895625000097","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
This paper is a survey of results and problems related to the following question: is it true that if G is a tournament with sufficiently large chromatic number, then G has two vertex-disjoint subtournaments , both with large chromatic number, such that all edges between them are directed from A to B? We describe what we know about this question, and report some progress on several other related questions, on tournament colouring and domination.
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.
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