Tverberg定理、圆盘和哈密顿圈
Tverberg's theorem, disks, and Hamiltonian cycles
摘要：
对于平面上的有限集$S$和顶点在$S$上的图，考虑由边诱导直径的圆盘。我们证明了对于任何奇数集$S$，存在一个哈密顿圈，这些磁盘共享一个点，并为偶数集$S$存在一个具有相同性质的Hamilton路。我们将讨论这些定理的高维版本及其与离散几何中其他结果的关系。
英文摘要：
For a finite set $S$ of points in the plane and a graph with vertices on $S$ consider the disks with diameters induced by the edges. We show that for any odd set $S$ there exists a Hamiltonian cycle for which these disks share a point, and for an even set $S$ there exists a Hamiltonian path with the same property. We discuss high-dimensional versions of these theorems and their relation to other results in discrete geometry.
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