{"title":"The largest hole in sparse random graphs","authors":"Nemanja Draganic, Stefan Glock, M. Krivelevich","doi":"10.1002/rsa.21078","DOIUrl":null,"url":null,"abstract":"We show that for any d=d(n) with d0(ϵ)≤d=o(n) , with high probability, the size of a largest induced cycle in the random graph G(n,d/n) is (2±ϵ)ndlogd . This settles a long‐standing open problem in random graph theory.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/rsa.21078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We show that for any d=d(n) with d0(ϵ)≤d=o(n) , with high probability, the size of a largest induced cycle in the random graph G(n,d/n) is (2±ϵ)ndlogd . This settles a long‐standing open problem in random graph theory.
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