The densest subgraph problem in sparse random graphs

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 Erdős–Rényi model, where it settles a conjecture of Hajek [IEEE Trans. Inform. Theory 36 (1990) 1398–1414]. 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 [In Probability on Discrete Structures (2004) 1–72 Springer].
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Article dans une revue
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2016, 26 (1), pp.305-327
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https://hal.archives-ouvertes.fr/hal-01361829
Contributeur : Serena Benassù <>
Soumis le : mercredi 7 septembre 2016 - 15:51:06
Dernière modification le : jeudi 27 avril 2017 - 09:47:00

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  • HAL Id : hal-01361829, version 1

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Justin Salez, Venkat Anantharam. The densest subgraph problem in sparse random graphs. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2016, 26 (1), pp.305-327. 〈hal-01361829〉

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