构造密集无网格线性3图

arXiv: Combinatorics Pub Date : 2020-10-27 DOI:10.1090/PROC/15673

Lior Gishboliner, A. Shapira

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引用次数: 9

摘要

我们证明了存在具有$n$顶点和$\Omega(n^2)$边的线性$3$-均匀超图，它不包含$3 \乘以3$网格的副本。这在F\ \ {u}redi和Ruszink\ \ {o}的一个猜想上取得了重大进展。我们还讨论了$(9,6)$ Brown-Erd\H{o} - s \'{o}s问题下界的证明以及关于Solymosi和Solymosi问题的证明的联系。

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Constructing dense grid-free linear 3-graphs

We show that there exist linear $3$-uniform hypergraphs with $n$ vertices and $\Omega(n^2)$ edges which contain no copy of the $3 \times 3$ grid. This makes significant progress on a conjecture of F\"{u}redi and Ruszink\'{o}. We also discuss connections to proving lower bounds for the $(9,6)$ Brown-Erd\H{o}s-S\'{o}s problem and to a problem of Solymosi and Solymosi.

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来源期刊

arXiv: Combinatorics

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