{"title":"Schreier图的Borel分数着色","authors":"Anton Bernshteyn","doi":"10.5802/ahl.145","DOIUrl":null,"url":null,"abstract":". Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ ý 2 Γ (with respect to some finite subset F Ď Γ). We show that the Borel fractional chromatic number of G is equal to 1 over the measurable independence number of G . As a consequence, we asymptotically determine the Borel fractional chromatic number of G when Γ is the free group, answering a question of Meehan.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Borel fractional colorings of Schreier graphs\",\"authors\":\"Anton Bernshteyn\",\"doi\":\"10.5802/ahl.145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ ý 2 Γ (with respect to some finite subset F Ď Γ). We show that the Borel fractional chromatic number of G is equal to 1 over the measurable independence number of G . As a consequence, we asymptotically determine the Borel fractional chromatic number of G when Γ is the free group, answering a question of Meehan.\",\"PeriodicalId\":192307,\"journal\":{\"name\":\"Annales Henri Lebesgue\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Lebesgue\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/ahl.145\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Lebesgue","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/ahl.145","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ ý 2 Γ (with respect to some finite subset F Ď Γ). We show that the Borel fractional chromatic number of G is equal to 1 over the measurable independence number of G . As a consequence, we asymptotically determine the Borel fractional chromatic number of G when Γ is the free group, answering a question of Meehan.
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