Asymptotic dimension of intersection graphs
Combinatorics
2022-10-05 v2
Abstract
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.
Cite
@article{arxiv.2202.07293,
title = {Asymptotic dimension of intersection graphs},
author = {Zdeněk Dvořák and Sergey Norin},
journal= {arXiv preprint arXiv:2202.07293},
year = {2022}
}
Comments
11 pages, no figures; v2: post-review version, 12 pages, 1 figure