Large Induced Matchings in Random Graphs

Oliver Cooley, Nemanja Dragani, Mihyun Kang, Benny Sudakov

Research output: Contribution to journalArticle

Abstract

Given a large graph H, does the binomial random graph G(n, p) contain a copy of H as an induced subgraph with high probability? This classical question has been studied extensively for various graphs H, going back to the study of the independence number of G(n, p) by Erd\H os and Bollob\'as and by Matula in 1976. In this paper we prove an asymptotically best possible result for induced matchings by showing that if C/n \leq p \leq 0.99 for some large constant C, then G(n, p) contains an induced matching of order approximately 2 logq(np), where q = 1 1 p .

Original languageEnglish
Pages (from-to)267-280
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Volume35
Issue number1
DOIs
Publication statusPublished - 22 Feb 2021

Keywords

  • Induced matchings
  • Paley-zygmund inequality
  • Random graphs
  • Talagrand's inequality

ASJC Scopus subject areas

  • Mathematics(all)

Fields of Expertise

  • Information, Communication & Computing

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