On the non-planarity of a random subgraph

Alan Frieze; Michael Krivelevich

doi:10.1017/S0963548313000308

On the non-planarity of a random subgraph

Alan Frieze
, Michael Krivelevich

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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 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 language	English GB
Pages (from-to)	722-732
Number of pages	11
Journal	Combinatorics Probability and Computing
Volume	22
Issue number	5
DOIs	https://doi.org/10.1017/S0963548313000308
State	Published - Sep 2013

ASJC Scopus subject areas

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

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AB - 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.

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DO - 10.1017/S0963548313000308

M3 - مقالة

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JO - Combinatorics Probability and Computing

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On the non-planarity of a random subgraph

Abstract

ASJC Scopus subject areas

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