Proper Coloring of Geometric Hypergraphs
Combinatorics
2019-04-17 v2 Computational Geometry
Abstract
We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then such an m exists. We prove this in the special case when F is the family of all homothetic copies of a given convex polygon. We also study the problem in higher dimensions.
Cite
@article{arxiv.1612.02158,
title = {Proper Coloring of Geometric Hypergraphs},
author = {Balázs Keszegh and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1612.02158},
year = {2019}
}