English

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.

Keywords

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}
}
R2 v1 2026-06-24T10:39:56.233Z