  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.

Combinatorics;Quantum Physics