English

Convex polygons and separation of convex sets

Combinatorics 2023-01-04 v1

Abstract

We prove that for any collection F of n2n \ge 2 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.

Keywords

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}
}