{"title":"重新审视分割图——斯托林斯结构定理的简短证明","authors":"B. Krön","doi":"10.1515/gcc.2010.013","DOIUrl":null,"url":null,"abstract":"Abstract This is a short proof of the existence of finite sets of edges in graphs with more than one end, such that after removing them we obtain two components which are nested with all their isomorphic images. This was first done in “Cutting up graphs” [Dunwoody, Combinatorica 2: 15–23, 1982]. Together with a certain tree construction and some elementary Bass–Serre theory this yields a combinatorial proof of Stallings' theorem on the structure of finitely generated groups with more than one end.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"120 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"Cutting up graphs revisited – a short proof of Stallings' structure theorem\",\"authors\":\"B. Krön\",\"doi\":\"10.1515/gcc.2010.013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract This is a short proof of the existence of finite sets of edges in graphs with more than one end, such that after removing them we obtain two components which are nested with all their isomorphic images. This was first done in “Cutting up graphs” [Dunwoody, Combinatorica 2: 15–23, 1982]. Together with a certain tree construction and some elementary Bass–Serre theory this yields a combinatorial proof of Stallings' theorem on the structure of finitely generated groups with more than one end.\",\"PeriodicalId\":119576,\"journal\":{\"name\":\"Groups Complex. Cryptol.\",\"volume\":\"120 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Complex. Cryptol.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/gcc.2010.013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complex. Cryptol.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc.2010.013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Cutting up graphs revisited – a short proof of Stallings' structure theorem
Abstract This is a short proof of the existence of finite sets of edges in graphs with more than one end, such that after removing them we obtain two components which are nested with all their isomorphic images. This was first done in “Cutting up graphs” [Dunwoody, Combinatorica 2: 15–23, 1982]. Together with a certain tree construction and some elementary Bass–Serre theory this yields a combinatorial proof of Stallings' theorem on the structure of finitely generated groups with more than one end.
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