English

Regular induced subgraphs of a random graph

Combinatorics 2008-08-15 v1 Probability

Abstract

An old problem of Erd\H{o}s, 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.

Keywords

Cite

@article{arxiv.0808.2023,
  title  = {Regular induced subgraphs of a random graph},
  author = {Michael Krivelevich and Benny Sudakov and Nicholas Wormald},
  journal= {arXiv preprint arXiv:0808.2023},
  year   = {2008}
}
R2 v1 2026-06-21T11:10:26.200Z