Colouring the Sphere
Combinatorics
2012-01-04 v1 Quantum Physics
Abstract
Let be the graph with the points of the unit sphere in 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.
Cite
@article{arxiv.1201.0486,
title = {Colouring the Sphere},
author = {C. D. Godsil and J. Zaks},
journal= {arXiv preprint arXiv:1201.0486},
year = {2012}
}
Comments
This is a lightly corrected version of a 1988 research report. This report has actually been cited more than once because of a connection to the Kochen-Specker theorem in physics and, after due deliberation, we have decided that it would be useful to post it on the arXiv