A characterisation of 3-colourable 3-dimensional triangulations
Combinatorics
2023-06-22 v2
Abstract
We extend Heawood's theorem on the colourability of plane triangulations to triangulations of 3-space. We prove that a triangulation of 3-space can be edge coloured with three colours if and only if all edges have even degree.
Cite
@article{arxiv.2204.02858,
title = {A characterisation of 3-colourable 3-dimensional triangulations},
author = {Johannes Carmesin and Emily Nevinson and Bethany Saunders},
journal= {arXiv preprint arXiv:2204.02858},
year = {2023}
}