On the edge-chromatic number of 2-complexes
Combinatorics
2024-11-13 v2 Geometric Topology
Abstract
We propose an open question that seeks to generalise the Four Colour Theorem from two to three dimensions. As an appetiser, we show that 12 instead of four colours are both sufficient and necessary to colour every 2-complex that embeds in a prescribed 3-manifold. However, our example of a 2-complex that requires 12 colours is not simplicial.
Cite
@article{arxiv.2310.16905,
title = {On the edge-chromatic number of 2-complexes},
author = {Jan Kurkofka and Emily Nevinson},
journal= {arXiv preprint arXiv:2310.16905},
year = {2024}
}
Comments
7 pages, 3 figures