An efficient container lemma
Combinatorics
2020-12-11 v2
Abstract
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.
Cite
@article{arxiv.1910.09208,
title = {An efficient container lemma},
author = {József Balogh and Wojciech Samotij},
journal= {arXiv preprint arXiv:1910.09208},
year = {2020}
}
Comments
56 pages, revised version