A characterisation of 3-colourable 3-dimensional triangulations

2022/04/06 by Carmesin, Johannes, Nevinson, Emily, Saunders, Bethany
#05C10 #05C15 #05E45 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.02858

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.

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