On the non-planarity of a random subgraph

Alan Frieze, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review


Let G be a finite graph with minimum degree r. Form a random subgraph Gp of G by taking each edge of G into Gp independently and with probability p. We prove that for any constant Î > 0, if p=\frac{1+\epsilon}{r} then Gp is non-planar with probability approaching 1 as r grows. This generalizes classical results on planarity of binomial random graphs.

Original languageEnglish
Pages (from-to)722-732
Number of pages11
JournalCombinatorics Probability and Computing
Issue number5
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

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


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