有效区分局部有限图中的所有缠结

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-03-21 DOI:10.1016/j.jctb.2024.03.004

Raphael W. Jacobs, Paul Knappe

{"title":"有效区分局部有限图中的所有缠结","authors":"Raphael W. Jacobs, Paul Knappe","doi":"10.1016/j.jctb.2024.03.004","DOIUrl":null,"url":null,"abstract":"<div><p>While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits such a tree-decomposition, in fact a canonical one. Our proof exhibits a thick end at any obstruction to the existence of such tree-decompositions and builds on new methods for the analysis of the limit behaviour of strictly increasing sequences of separations.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"167 ","pages":"Pages 189-214"},"PeriodicalIF":1.2000,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000224/pdfft?md5=eb127aa3ba243eafd76779abff8b1e9d&pid=1-s2.0-S0095895624000224-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Efficiently distinguishing all tangles in locally finite graphs\",\"authors\":\"Raphael W. Jacobs, Paul Knappe\",\"doi\":\"10.1016/j.jctb.2024.03.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits such a tree-decomposition, in fact a canonical one. Our proof exhibits a thick end at any obstruction to the existence of such tree-decompositions and builds on new methods for the analysis of the limit behaviour of strictly increasing sequences of separations.</p></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":\"167 \",\"pages\":\"Pages 189-214\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0095895624000224/pdfft?md5=eb127aa3ba243eafd76779abff8b1e9d&pid=1-s2.0-S0095895624000224-main.pdf\",\"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/S0095895624000224\",\"RegionNum\":1,\"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":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895624000224","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: 0

摘要

有限图具有能有效区分其所有纠结的树形分解，而具有粗末端的局部有限图则不需要这样的树形分解。我们证明，每一个没有粗末端的局部有限图都有这样的树形分解，事实上是一个典型的树形分解。我们的证明展示了在任何阻碍这种树形分解存在的障碍处的厚末端，并建立在分析严格递增分离序列的极限行为的新方法之上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Efficiently distinguishing all tangles in locally finite graphs

While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits such a tree-decomposition, in fact a canonical one. Our proof exhibits a thick end at any obstruction to the existence of such tree-decompositions and builds on new methods for the analysis of the limit behaviour of strictly increasing sequences of separations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

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.