A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane
Combinatorics
2026-08-05 v1
Abstract
With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years. While most constructions rely heavily on the Moser spindle, Voronov \textit{et al.} found examples on 64513 vertices that completely avoid it. In this note, we improve upon this result by presenting a 5-chromatic unit distance graph on 2131 vertices that similarly does not contain the Moser spindle. It is constructed utilizing the arcs of a 7-fold symmetric unit distance graph on 21 vertices.
Keywords
Cite
@article{arxiv.2608.04542,
title = {A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane},
author = {Jan Kristian Haugland},
journal= {arXiv preprint arXiv:2608.04542},
year = {2026}
}
Comments
7 pages, 2 figures