Tverberg图的一个局部判别法
A local criterion for Tverberg graphs
摘要：
拓扑Tverberg定理指出，对于任何一个从（d+1）（q-1）-单形到R}^d的连续映射，对q个素幂q，有q个像相交的单形的不相交面F_i。可以对允许单形的顶点对在同一面F_i上设置条件。如果拓扑Tverberg定理仍然成立，则一个图的顶点集与单纯形的顶点集相同，且如果两个顶点不属于同一个Fi，则两个顶点相邻，称为Tverberg图。Hell，Schoneborn和Ziegler研究了这些图，并且已知小路，圈和完全图的不交并都是Tverberg图。我们发现了许多新的例子，建立一个局部的标准图是Tverberg。我们的主要定理的一个简单的推论是，如果一个图的最大度是D，并且D（D+1）<q，那么它是一个Tverberg图。我们陈述了结果的仿射版本，并描述了如何使用它们来枚举Tverberg分区。
英文摘要：
The topological Tverberg theorem states that for any prime power q and continuous map from a (d+1)(q-1)-simplex to R}^d, there are q disjoint faces F_i of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the same face F_i. A graph with the same vertex set as the simplex, and with two vertices adjacent if they should not be in the same F_i, is called a Tverberg graph if the topological Tverberg theorem still work. These graphs have been studied by Hell, Schoneborn and Ziegler, and it is known that disjoint unions of small paths, cycles, and complete graphs are Tverberg graphs. We find many new examples by establishing a local criterion for a graph to be Tverberg. An easily stated corollary of our main theorem is that if the maximal degree of a graph is D, and D(D+1)<q, then it is a Tverberg graph. We state the affine versions of our results and also describe how they can be used to enumerate Tverberg partitions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
