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On the Non-Planarity of a Random Subgraph
journal contribution
posted on 2013-06-24, 00:00 authored by Alan FriezeAlan Frieze, Michael KrivelevichLet G be a finite graph with minimum degree r. Form a random subgraph Gp of G by taking each edge of G into Gpindependently and with probability p. We prove that for any constant ε > 0, if , then Gp is non-planar with probability approaching 1 as r grows. This generalizes classical results on planarity of binomial random graphs.