{"title":"Maximum chordal subgraphs of random graphs","authors":"Michael Krivelevich, Maksim Zhukovskii","doi":"10.1017/s0963548324000154","DOIUrl":null,"url":null,"abstract":"We find asymptotics of the maximum size of a chordal subgraph in a binomial random graph <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000154_inline1.png\"/> <jats:tex-math> $G(n,p)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000154_inline2.png\"/> <jats:tex-math> $p=\\mathrm{const}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000154_inline3.png\"/> <jats:tex-math> $p=n^{-\\alpha +o(1)}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":10503,"journal":{"name":"Combinatorics, Probability and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorics, Probability and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0963548324000154","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We find asymptotics of the maximum size of a chordal subgraph in a binomial random graph $G(n,p)$ , for $p=\mathrm{const}$ and $p=n^{-\alpha +o(1)}$ .
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