A 5-chromatic same-distance graph in the hyperbolic plane
Combinatorics
2023-03-14 v1
Abstract
The chromatic number of the plane problem asks for the minimum number of colors so that each point of the plane can be assigned a single color with the property that no two points unit-distance apart are identically colored. It is now known that the answer is 5, 6, or 7. Here we consider the problem in the context of the hyperbolic plane. We prove that there exists a distance so that every 4-coloring of the hyperbolic plane contains two points distance apart, which are identically colored.
Cite
@article{arxiv.2303.06801,
title = {A 5-chromatic same-distance graph in the hyperbolic plane},
author = {Geoffrey Exoo and Dan Ismailescu},
journal= {arXiv preprint arXiv:2303.06801},
year = {2023}
}