Key points are not available for this paper at this time.
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.
Anantharam et al. (2016) studied this question.