Hypergraphs with minimum positive uniform Turán density

2021/05/20 by Frederik Garbe, Garbe, Frederik, Daniel Král͏̌ +3 · 3 citations
Mathematics · #05C65 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2105.09883

openalex publication_date 2021/05/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Reiher, Rödl and Schacht [J. London Math. Soc. 97 (2018), 77--97] showed that the uniform Turán density of every 3-uniform hypergraph is either 0 or at least 1/27, and asked whether there exist 3-uniform hypergraphs with uniform Turán density equal or arbitrarily close to 1/27. We construct 3-uniform hypergraphs with uniform Turán density equal to 1/27.

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