Hypergraphs without complete partite subgraphs
Combinatorics
2026-05-20 v2
Abstract
Fix integers and and set . Let denote the complete -partite -uniform hypergraph with parts of size . We prove that the Zarankiewicz number provided . Previously this was known only for due to Pohoata and Zakharov. Our novel approach, which uses Behrend's construction of sets with no 3 term arithmetic progression, also applies for small values of , for example, it gives where the exponent 11/4 is optimal, whereas previously this was only known with 7 replaced by 721.
Cite
@article{arxiv.2507.06390,
title = {Hypergraphs without complete partite subgraphs},
author = {Dhruv Mubayi},
journal= {arXiv preprint arXiv:2507.06390},
year = {2026}
}
Comments
6 pages