Convex polygons and separation of convex sets
Combinatorics
2023-01-04 v1
Abstract
We prove that for any collection F of pairwise disjoint compact convex sets in the plane there is a pair of sets A and B in F such that any line that separates A from B separates either A or B from a subcollection of F with at least n/18 sets.
Cite
@article{arxiv.2209.11988,
title = {Convex polygons and separation of convex sets},
author = {Eduardo Rivera-Campo and Jorge Urrutia},
journal= {arXiv preprint arXiv:2209.11988},
year = {2023}
}