论文标题
Tverberg的定理，磁盘和哈密顿周期
Tverberg's theorem, disks, and Hamiltonian cycles
论文作者
论文摘要
对于飞机上的有限设置$ s $点，以及在$ s $上的顶点的图形，请考虑边缘引起的直径的磁盘。我们表明，对于任何奇数$ s $，都存在一个汉密尔顿周期，这些磁盘可以共享一个点，并且对于偶数$ s $，存在同一属性的汉密尔顿路径。我们讨论这些定理的高维版本及其与离散几何形状的其他结果的关系。
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.
