Largest sparse subgraphs of random graphs

Nikolaos Fountoulakis*, Ross J. Kang, Colin McDiarmid

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For the Erdos-Rényi random graph Gn,p, we consider the order of a largest vertex subset that induces a subgraph with average degree at most t. For the case when both p and t are fixed, this value is asymptotically almost surely concentrated on at most two explicitly given points. This generalises a result on the independence number of random graphs. For both the upper and lower bounds, we rely on large deviations inequalities for the binomial distribution.

Original languageEnglish
Pages (from-to)349-354
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume38
DOIs
Publication statusPublished - 1 Dec 2011

Bibliographical note

Funding Information:
Acknowledgement. Part of this research was conducted while RJK was a NSERC Postdoctoral Fellow at McGill University; he is currently supported by the EPSRC, grant EP/G066604/1.

Keywords

  • Independence number
  • Large deviations
  • Random graphs
  • Sparse subgraphs
  • Two-point concentration

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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