Abstract
AbstractAn old problem of Erdős, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on $n$ vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on $n$ vertices, i.e., in a binomial random graph $G(n,1/2)$. We prove that with high probability a largest induced regular subgraph of $G(n,1/2)$ has about $n^{2/3}$ vertices. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 235–250, 2011
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