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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Submitted on : Wednesday, September 7, 2016 - 3:51:06 PM
Last modification on : Sunday, March 31, 2019 - 1:40:23 AM

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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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