{"title":"纠缠","authors":"Johannes Carmesin , Jan Kurkofka","doi":"10.1016/j.jctb.2023.08.007","DOIUrl":null,"url":null,"abstract":"<div><p>Robertson and Seymour constructed for every graph <em>G</em> a tree-decomposition that efficiently distinguishes all the tangles in <em>G</em>. While all previous constructions of these decompositions are either iterative in nature or not canonical, we give an explicit one-step construction that is canonical.</p><p>The key ingredient is an axiomatisation of ‘local properties’ of tangles. Generalisations to locally finite graphs and matroids are also discussed.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"164 ","pages":"Pages 17-28"},"PeriodicalIF":1.2000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Entanglements\",\"authors\":\"Johannes Carmesin , Jan Kurkofka\",\"doi\":\"10.1016/j.jctb.2023.08.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Robertson and Seymour constructed for every graph <em>G</em> a tree-decomposition that efficiently distinguishes all the tangles in <em>G</em>. While all previous constructions of these decompositions are either iterative in nature or not canonical, we give an explicit one-step construction that is canonical.</p><p>The key ingredient is an axiomatisation of ‘local properties’ of tangles. Generalisations to locally finite graphs and matroids are also discussed.</p></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":\"164 \",\"pages\":\"Pages 17-28\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-01-01\",\"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/S0095895623000680\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/9/13 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895623000680","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/9/13 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Robertson and Seymour constructed for every graph G a tree-decomposition that efficiently distinguishes all the tangles in G. While all previous constructions of these decompositions are either iterative in nature or not canonical, we give an explicit one-step construction that is canonical.
The key ingredient is an axiomatisation of ‘local properties’ of tangles. Generalisations to locally finite graphs and matroids are also discussed.
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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