论文标题
同源物的通用指数
A universal exponent for homeomorphs
论文作者
论文摘要
We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex $S$: any $n$-vertex two-dimensional complex with at least $C_S n^{3-1/5}$ facets contains a homeomorphic copy of $S$, where $C_S > 0$ is an absolute constant depending on $S$ alone.这个结果是Mader对一维复合物的经典结果的二维类似物，从2006年开始阐明了旧的外线问题。
We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex $S$: any $n$-vertex two-dimensional complex with at least $C_S n^{3-1/5}$ facets contains a homeomorphic copy of $S$, where $C_S > 0$ is an absolute constant depending on $S$ alone. This result, a two-dimensional analogue of a classical result of Mader for one-dimensional complexes, sheds some light on an old problem of Linial from 2006.
