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A universal exponent for homeomorphs
Israel Journal of Mathematics ( IF 1 ) Pub Date : 2021-06-08 , DOI: 10.1007/s11856-021-2156-7
Peter Keevash , Jason Long , Bhargav Narayanan , Alex Scott

We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex S: any two-dimensional complex on n vertices with at least CSn3−1/5 facets contains a homeomorph of S, where CS > 0 is a constant depending on S alone. This result, a two-dimensional analogue of a classical one-dimensonal result of Mader, sheds some light on an old problem of Linial from 2006.



中文翻译:

同胚的通用指数

我们证明了任意二维单纯复形S的拓扑图兰数的统一边界:n个顶点上至少具有C S n 3-1/5个面的任何二维复形包含S的同胚,其中C S > 0 是仅取决于S的常数。这个结果是 Mader 的经典一维结果的二维模拟,揭示了 2006 年 Linial 的一个老问题。

更新日期:2021-06-08
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