Largest sparse subgraphs of random graphs

Abstract

For the Erdős-Rényi random graph Gn,p, we give a precise asymptotic formula for the size α̂t(Gn,p) of a largest vertex subset inGn,p that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t = t(n) is not too large. In the case of fixed t and p, we find that this value is asymptotically almost surely concentrated… (More)
DOI: 10.1016/j.endm.2011.09.057
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