On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three
Combinatorics
2025-11-13 v1
Abstract
We provide a simplified proof of the following special case of Wegner's conjecture: every planar graph of maximum degree at most three admits a distance-2 coloring with at most eight colors. Our main contribution is significant simplification of the most technically challenging part of Wegner's proof: the case involving the removal of a 5-cycle.
Cite
@article{arxiv.2511.09391,
title = {On Wegner's 8-Coloring Theorem for Planar Graphs of Maximum Degree Three},
author = {Gabriel Elvin and Hajrudin Fejzić and Youngsu Kim},
journal= {arXiv preprint arXiv:2511.09391},
year = {2025}
}