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On the Non-Planarity of a Random Subgraph

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journal contribution
posted on 24.06.2013, 00:00 authored by Alan FriezeAlan Frieze, Michael Krivelevich

Let 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.


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