{"title":"Rational Exponents Near Two","authors":"D. Conlon, Oliver Janzer","doi":"10.19086/aic.2022.9","DOIUrl":null,"url":null,"abstract":"A longstanding conjecture of Erd˝os and Simonovits states that for every rational r between 1 and 2 there is a graph H such that the largest number of edges in an H-free graph on n vertices is Q(nr). Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form 2a=b with b sufficiently large in terms of a.","PeriodicalId":36338,"journal":{"name":"Advances in Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19086/aic.2022.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 5
Abstract
A longstanding conjecture of Erd˝os and Simonovits states that for every rational r between 1 and 2 there is a graph H such that the largest number of edges in an H-free graph on n vertices is Q(nr). Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form 2a=b with b sufficiently large in terms of a.
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