论文标题
交叉图的渐近维度
Asymptotic dimension of intersection graphs
论文作者
论文摘要
我们表明，有界纵横比的r^n中紧凑型凸的相交图最多具有2N+1的渐近维度。更一般而言，我们证明，对于满足以下条件的Assouad-nagata维度的任何度量空间的系统系统的相交图就是这种情况：对于每个R，S> 0和每个点P，每个点P，直径s的成对分散元件的数量至少在p lave p lage p lage p lage p lage p lage p lage p take p lage c lim/r/s的函数均在r/s函数上均具有r/s的功能。
We show that intersection graphs of compact convex sets in R^n of bounded aspect ratio have asymptotic dimension at most 2n+1. More generally, we show this is the case for intersection graphs of systems of subsets of any metric space of Assouad-Nagata dimension n that satisfy the following condition: For each r,s>0 and every point p, the number of pairwise-disjoint elements of diameter at least s in the system that are at distance at most r from p is bounded by a function of r/s.
