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arXiv · 1312.4494

The densest subgraph problem in sparse random graphs

Venkat Anantharam·Justin Salez
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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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Venkat Anantharam, Justin Salez. 2016-01-07. The densest subgraph problem in sparse random graphs. https://doi.org/10.1214/14-aap1091

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