Jakub Gajarsk'y, Michal Pilipczuk, Szymon Toruńczyk
{"title":"Stable graphs of bounded twin-width","authors":"Jakub Gajarsk'y, Michal Pilipczuk, Szymon Toruńczyk","doi":"10.1145/3531130.3533356","DOIUrl":null,"url":null,"abstract":"We prove that every class of graphs that is monadically stable and has bounded twin-width can be transduced from some class with bounded sparse twin-width. This generalizes analogous results for classes of bounded linear cliquewidth [Nešetřil et al. 2021b] and of bounded cliquewidth [Nešetřil et al. 2021a]. It also implies that monadically stable classes of bounded twin-width are linearly χ-bounded.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3531130.3533356","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 23
Abstract
We prove that every class of graphs that is monadically stable and has bounded twin-width can be transduced from some class with bounded sparse twin-width. This generalizes analogous results for classes of bounded linear cliquewidth [Nešetřil et al. 2021b] and of bounded cliquewidth [Nešetřil et al. 2021a]. It also implies that monadically stable classes of bounded twin-width are linearly χ-bounded.
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