Constructing Dense Grid-Free Linear 3-Graphs

2020/10/27 by Gishboliner, Lior, Shapira, Asaf · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.14469

Abstract

We show that there exist linear 3-uniform hypergraphs with n vertices and Ω(n²) edges which contain no copy of the 3 × 3 grid. This makes significant progress on a conjecture of Füredi and Ruszinkó. We also discuss connections to proving lower bounds for the (9,6) Brown-Erdős-Sós problem and to a problem of Solymosi and Solymosi.

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• Ramsey numbers of digraphs with local edge structure

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