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On the Non-Planarity of a Random Subgraph

Published online by Cambridge University Press:  22 July 2013

ALAN FRIEZE  and
MICHAEL KRIVELEVICH
ALAN FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213, USA (e-mail: alan@random.math.cmu.edu)
MICHAEL KRIVELEVICH
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: krivelev@post.tau.ac.il)
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Abstract

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 ε > 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.

Keywords

Primary 05C80Secondary 05C10
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 5 , September 2013 , pp. 722 - 732
Copyright
Copyright © Cambridge University Press 2013 

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