{"title":"稀疏随机图中的最大诱导树","authors":"J. C. Buitrago Oropeza","doi":"10.1134/S1064562424701989","DOIUrl":null,"url":null,"abstract":"<p>We prove that for any <span>\\(\\varepsilon > 0\\)</span> and <span>\\({{n}^{{ - \\frac{{e - 2}}{{3e - 2}} + \\varepsilon }}} \\leqslant p = o(1)\\)</span> the maximum size of an induced subtree of the binomial random graph <span>\\(G(n,p)\\)</span> is concentrated asymptotically almost surely at two consecutive points.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximum Induced Trees in Sparse Random Graphs\",\"authors\":\"J. C. Buitrago Oropeza\",\"doi\":\"10.1134/S1064562424701989\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that for any <span>\\\\(\\\\varepsilon > 0\\\\)</span> and <span>\\\\({{n}^{{ - \\\\frac{{e - 2}}{{3e - 2}} + \\\\varepsilon }}} \\\\leqslant p = o(1)\\\\)</span> the maximum size of an induced subtree of the binomial random graph <span>\\\\(G(n,p)\\\\)</span> is concentrated asymptotically almost surely at two consecutive points.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1064562424701989\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424701989","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
AbstractWe prove that for any \(\varepsilon > 0\) and\({{n}^{ - \frac{{e - 2}}{{3e - 2}})+ \varepsilon }}}\二项式随机图 \(G(n,p)\) 的诱导子树的最大尺寸几乎肯定地集中在两个连续点上。
We prove that for any \(\varepsilon > 0\) and \({{n}^{{ - \frac{{e - 2}}{{3e - 2}} + \varepsilon }}} \leqslant p = o(1)\) the maximum size of an induced subtree of the binomial random graph \(G(n,p)\) is concentrated asymptotically almost surely at two consecutive points.
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