论文标题
图形的笛卡尔产品数量
The Turán number of the Cartesian product of graphs
论文作者
论文摘要
最近，Domagojbradač，Oliver Janzer，Benny Sudakov和IstvánTomon已证明，Turán的$ 2 $二维网格为$θ（n^{3/2}）$，或更多一般性，$ \ \ \ \ \ \\ Mathrm {ex} {ex} $ t $是一棵非平凡的树，$ p $是一种非平凡的路径，$ t \ square {p} $表示笛卡尔产品。在他们的证明中，他们展示了一种新颖的方法，它使用了张量的功率技巧，该技巧在Turán型问题中具有很大的潜力。在证明结束时，他们猜想非平地树$ t $ and $ t $和$ r $，$ \ mathrm {ex} \ left（n，t \ square {r} \ right）=θ（n^{3/2}）$。本文是基于他们的工作的扩展，我们通过调整方法来成功证明了上述猜想。
Recently, Domagoj Bradač, Oliver Janzer, Benny Sudakov and István Tomon have proved that the Turán number of $2$-dimensional grids is $Θ(n^{3/2})$, or more general, $\mathrm{ex}\left(n,T\square{P}\right)=Θ(n^{3/2})$, where $T$ is a non-trivial tree, $P$ is a non-trivial path, and $T\square{P}$ denotes the Cartesian product. In their proof, they exhibited a novel way of using the tensor power trick, which has lots of potential in Turán type problems. By the end of their proof, they conjectured that $\mathrm{ex}\left(n,T\square{R}\right)=Θ(n^{3/2})$ for non-trivial trees $T$ and $R$. This paper is an extension based on their work, we successfully prove the above conjecture by adapting their approach.
