Largest sparse subgraphs of random graphs

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes

External organisations

  • Durham University
  • University of Oxford


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.

Bibliographic 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.


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


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