An Efficient Container Lemma

József Balogh, Wojciech Samotij

Research output: Contribution to journalArticlepeer-review


We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional convex geometry. The existence of smaller families of containers for independent sets in such hypergraphs, which is guaranteed by the new theorem, allows us to improve upon the best currently known bounds for several problems in extremal graph theory, discrete geometry, and Ramsey theory.

Original languageEnglish
Article number17
Number of pages56
JournalDiscrete Analysis
StatePublished - 2020


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