The Turán number of surfaces

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-10-18 DOI:10.1112/blms.13167

Maya Sankar

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Abstract

We show that there is a constant $c$ such that any 3-uniform hypergraph $H$ with $n$ vertices and at least $c n^{5 / 2}$ 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.

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Turán曲面数

我们证明了存在一个常数c$ c$，使得任何3-一致超图H ${\mathcal {H}}$具有n$ n$顶点且至少c$ n 5 / 2$cn^{5/2}$ edges包含实投影平面的三角剖分作为子图。这就解决了库帕夫斯基、波利安斯基、托蒙和扎哈罗夫的一个猜想。此外，我们的工作，结合先前的结果，渐近地确定了Turán所有曲面的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊