Colouring the Sphere

Details Colouring the Sphere Colouring the Sphere

2012-01-02

arxiv.org/abs/1201.0486v1

Mathematics

Combinatorics

This is a lightly corrected version of a 1988 research report. This report has actually been cited more than once because of a

Scientific paper

Let $G$ be the graph with the points of the unit sphere in $\mathbb{R}^3$ as
its vertices, by defining two unit vectors to be adjacent if they are
orthogonal as vectors. We present a proof, based on work of Hales and Straus
chromatic number of this graph is four. We also prove that the subgraph of G
induced by the unit vectors with rational coordinates is 3-colourable.

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