Regular induced subgraphs of a random Graph

An old problem of Erd˝os, 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 n2/3 vertices.

• Type: Journal
• Year: 2011
• Where: RSA
• Authors: Michael Krivelevich, Benny Sudakov, Nicholas C. Wormald
• Keywords: Binomial Random Graph, Regular Subgraph, RSA 2011, Typical Graph