论文标题
Turán的表面数量
The Turán Number of Surfaces
论文作者
论文摘要
我们表明有一个常数的$ c $，使得带有$ n $ Vertices的任何3均匀的HyperGraph $ \ Mathcal H $，至少$ CN^{5/2} $ edges包含对真实投射平面的三角剖分。这解决了Kupavskii，Polyanskii，Tomon和Zakharov的猜想。此外，我们的工作与先前的结果相结合，渐近地确定了所有表面的Turán数量。
We show that there is a constant $c$ such that any 3-uniform hypergraph $\mathcal H$ with $n$ vertices and at least $cn^{5/2}$ edges contains a triangulation of the real projective plane as a subgraph. This resolves a conjecture of Kupavskii, Polyanskii, Tomon, and Zakharov. Furthermore, our work, combined with prior results, asymptotically determines the Turán number of all surfaces.
