{"title":"诱导子图和树分解 XIV.洞中的非相邻邻图","authors":"Maria Chudnovsky , Sepehr Hajebi , Sophie Spirkl","doi":"10.1016/j.ejc.2024.104074","DOIUrl":null,"url":null,"abstract":"<div><div>A <em>clock</em> is a graph consisting of an induced cycle <span><math><mi>C</mi></math></span> and a vertex not in <span><math><mi>C</mi></math></span> with at least two non-adjacent neighbours in <span><math><mi>C</mi></math></span>. We show that every clock-free graph of large treewidth contains a “basic obstruction” of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001598/pdfft?md5=fa98c8a13265d848775c4b52beb995da&pid=1-s2.0-S0195669824001598-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole\",\"authors\":\"Maria Chudnovsky , Sepehr Hajebi , Sophie Spirkl\",\"doi\":\"10.1016/j.ejc.2024.104074\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A <em>clock</em> is a graph consisting of an induced cycle <span><math><mi>C</mi></math></span> and a vertex not in <span><math><mi>C</mi></math></span> with at least two non-adjacent neighbours in <span><math><mi>C</mi></math></span>. We show that every clock-free graph of large treewidth contains a “basic obstruction” of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall.</div></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0195669824001598/pdfft?md5=fa98c8a13265d848775c4b52beb995da&pid=1-s2.0-S0195669824001598-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0195669824001598\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669824001598","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole
A clock is a graph consisting of an induced cycle and a vertex not in with at least two non-adjacent neighbours in . We show that every clock-free graph of large treewidth contains a “basic obstruction” of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall.
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.
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