Regular induced subgraphs of a random Graph

Michael Krivelevich, Benny Sudakov, Nicholas Wormald
2011 Random structures & algorithms (Print)  
An 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.
doi:10.1002/rsa.20324 fatcat:pdu2no663bfcrdjheuur6aqipe