THE METHOD OF HYPERGRAPH CONTAINERS

By Jozsef Balogh, Robert Morris, Wojciech Samotij. International Congress of Mathematicans, 2018

80 citations recorded by the source corpus.

In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by the independent sets of uniform hypergraphs whose edges are sufficiently evenly distributed; more precisely, it provides a relatively small family of 'containers' for the independent sets, each of which contains few edges. We attempt to convey to the reader a general high-level overview of the method, focusing on a small number of illustrative applications in areas such as extremal graph theory, Ramsey theory, additive combinatorics, and discrete geometry, and avoiding technical details as much as possible.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/a60c06accb33367b7a1ff574e319a626f9aa611f