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Finding independent sets of maximum size in fixed graphs is well known to bean NP-hard task. Using scaling limits, we characterise the asymptotics ofsequential degree-greedy explorations and provide sufficient conditions forthis algorithm to find an independent set of asymptotically optimal size inlarge sparse random graphs with given degree sequences. In the special case ofsparse Erd\"os-R\'enyi graphs, our results allow to give a simple proof of theso-called $e$-phenomenon identified by Karp and Sipser for matchings and togive an alternative characterisation of the asymptotic independence number.

Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs