Understand
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.
Built on
Algebraic Projective Geometry
J. G. Semple and G. T. Kneebone · 1952
Earlier work this paper cites.
Similar
Projective colorings
A. W. Hales and E. G. Straus · 1982
Cited alongside, same era.
Then
Local fields
J. W. S. Cassels · 1986
Later among the works it cites.
Beyond the bibliography
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…