论文标题
线性超图的常规子图
Regular subgraphs of linear hypergraphs
论文作者
论文摘要
我们证明，$ n $ n $顶点的3-均匀线性超图中的最大边数为no no 2-repular subhypergraph为$ n^{1+o（1）} $。这解决了Dellamonica，Haxell，Luczak，Mubayi，Nagle，Person，Rödl，Schacht和Verstraëte的猜想。我们使用此结果表明，在$ 3 $均匀的超图中的最大边数在$ n $的顶点上，包含不浸入封闭表面的$ n^{2+o（1）} $。此外，我们在$ k $均匀的线性超图中介绍了最大边缘数量，其中包含$ r $ $ $ r $的subhypergraph。
We prove that the maximum number of edges in a 3-uniform linear hypergraph on $n$ vertices containing no 2-regular subhypergraph is $n^{1+o(1)}$. This resolves a conjecture of Dellamonica, Haxell, Luczak, Mubayi, Nagle, Person, Rödl, Schacht and Verstraëte. We use this result to show that the maximum number of edges in a $3$-uniform hypergraph on $n$ vertices containing no immersion of a closed surface is $n^{2+o(1)}$. Furthermore, we present results on the maximum number of edges in $k$-uniform linear hypergraphs containing no $r$-regular subhypergraph.
