Large complete minors in random subgraphs

Joshua Erde, Mihyun Kang, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review


Let G be a graph of minimum degree at least k and let Gp be the random subgraph of G obtained by keeping each edge independently with probability p. We are interested in the size of the largest complete minor that Gp contains when p = (1 + ε)/k with ε > 0. We show that with high probability Gp contains a complete minor of order Ω~ (k), where the ∼ hides a polylogarithmic factor. Furthermore, in the case where the order of G is also bounded above by a constant multiple of k, we show that this polylogarithmic term can be removed, giving a tight bound.

Original languageEnglish
Pages (from-to)619-630
Number of pages12
JournalCombinatorics Probability and Computing
Issue number4
StatePublished - Jul 2021

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics


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