35 research outputs found
On the edge-chromatic number of 2-complexes
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.Comment: 7 pages, 3 figure