On the Non-Planarity of a Random Subgraph

2013-06-24T00:00:00Z (GMT) by Alan 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.