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February 2016 The densest subgraph problem in sparse random graphs
Venkat Anantharam, Justin Salez
Ann. Appl. Probab. 26(1): 305-327 (February 2016). DOI: 10.1214/14-AAP1091


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. "The densest subgraph problem in sparse random graphs." Ann. Appl. Probab. 26 (1) 305 - 327, February 2016.


Received: 1 January 2014; Revised: 1 July 2014; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1336.60010
MathSciNet: MR3449319
Digital Object Identifier: 10.1214/14-AAP1091

Primary: 05C80 , 60C05
Secondary: 90B15

Keywords: load balancing , Local weak convergence , Maximum subgraph density , objective method , pairing model , unimodularity

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 1 • February 2016
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