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arXiv · 1203.0132

Largest sparse subgraphs of random graphs

Nikolaos Fountoulakis·Ross J. Kang·Colin McDiarmid
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Abstract

For the Erdős-Rényi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,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 on at most two explicitly given points. This generalises a result on the independence number of random graphs. For both the upper and lower bounds, we rely on large deviations inequalities for the binomial distribution.

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Nikolaos Fountoulakis, Ross J. Kang, Colin McDiarmid. 2012-03-01. Largest sparse subgraphs of random graphs. https://doi.org/10.1016/j.ejc.2013.06.012

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