The densest subgraph problem in sparse random graphs
Probability
2016-01-08 v2 Discrete Mathematics
Combinatorics
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-R\'{e}nyi 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].
Cite
@article{arxiv.1312.4494,
title = {The densest subgraph problem in sparse random graphs},
author = {Venkat Anantharam and Justin Salez},
journal= {arXiv preprint arXiv:1312.4494},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/14-AAP1091 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)