English

Dependent Random Choice

Combinatorics 2010-04-27 v2 Probability

Abstract

We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss some of them.

Keywords

Cite

@article{arxiv.0909.3271,
  title  = {Dependent Random Choice},
  author = {Jacob Fox and Benny Sudakov},
  journal= {arXiv preprint arXiv:0909.3271},
  year   = {2010}
}

Comments

32 pages

R2 v1 2026-06-21T13:47:38.644Z