{"title":"有界线性团宽图的可定义分解","authors":"M. Bojanczyk, Martin Grohe, Michal Pilipczuk","doi":"10.1145/3209108.3209135","DOIUrl":null,"url":null,"abstract":"We prove that for every positive integer k, there exists an MSO1-transduction that given a graph of linear cliquewidth at most k outputs, nondeterministically, some clique decomposition of the graph of width bounded by a function of k. A direct corollary of this result is the equivalence of the notions of CMSO1-definability and recognizability on graphs of bounded linear cliquewidth.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Definable decompositions for graphs of bounded linear cliquewidth\",\"authors\":\"M. Bojanczyk, Martin Grohe, Michal Pilipczuk\",\"doi\":\"10.1145/3209108.3209135\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that for every positive integer k, there exists an MSO1-transduction that given a graph of linear cliquewidth at most k outputs, nondeterministically, some clique decomposition of the graph of width bounded by a function of k. A direct corollary of this result is the equivalence of the notions of CMSO1-definability and recognizability on graphs of bounded linear cliquewidth.\",\"PeriodicalId\":389131,\"journal\":{\"name\":\"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3209108.3209135\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3209108.3209135","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Definable decompositions for graphs of bounded linear cliquewidth
We prove that for every positive integer k, there exists an MSO1-transduction that given a graph of linear cliquewidth at most k outputs, nondeterministically, some clique decomposition of the graph of width bounded by a function of k. A direct corollary of this result is the equivalence of the notions of CMSO1-definability and recognizability on graphs of bounded linear cliquewidth.
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