论文标题
构建密集的无网线性$ 3 $ -Graphs
Constructing Dense Grid-Free Linear $3$-Graphs
论文作者
论文摘要
我们表明，有线性$ 3 $ - 均匀的超图，带有$ n $顶点和$ω（n^2）$边缘，不包含$ 3 \ times 3 $ grid的副本。这在Füredi和Ruszinkó的猜想上取得了重大进展。我们还讨论了与$（9,6）$ brown-erdős-sós问题以及Solymosi和Solymosi的问题的相关连接。
We show that there exist linear $3$-uniform hypergraphs with $n$ vertices and $Ω(n^2)$ edges which contain no copy of the $3 \times 3$ 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.
