Dependent Random Choice
Jacob Fox, Benny Sudakov

TL;DR
This paper surveys a probabilistic technique called Dependent Random Choice, which helps find large vertex subsets with many common neighbors in dense graphs, with applications across various fields of combinatorics.
Contribution
It introduces and discusses the Dependent Random Choice technique and its recent impactful applications in multiple areas of combinatorics.
Findings
Effective in finding large subsets with common neighbors
Applied successfully in extremal graph theory and Ramsey theory
Facilitates new results in additive combinatorics and geometry
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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
