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The densest subgraph problem in sparse random graphs

Venkat Anantharam 1 Justin Salez 2, *
* Corresponding author
2 Modélisation stochastique
LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Abstract : We determine the asymptotic behavior of the maximum subgraph density of large random graphs with a prescribed degree sequence. The result applies in particular to the Erd\H{o}s-Rényi model, where it settles a conjecture of Hajek (1990). Our proof consists in extending the notion of balanced loads from finite graphs to their local weak limits, using unimodularity. This is a new illustration of the objective method described by Aldous and Steele (2004).
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Contributor : Justin Salez <>
Submitted on : Monday, December 16, 2013 - 12:04:43 PM
Last modification on : Friday, March 27, 2020 - 3:51:31 AM
Document(s) archivé(s) le : Tuesday, March 18, 2014 - 4:10:52 PM


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  • HAL Id : hal-00919079, version 1
  • ARXIV : 1312.4494


Venkat Anantharam, Justin Salez. The densest subgraph problem in sparse random graphs. 2013. ⟨hal-00919079⟩



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