Asymptotic dimension of intersection graphs

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. (c) 2022 Elsevier Ltd. All rights reserved.