Colouring the Sphere

2012/01/02 by Godsil, C. D., Zaks, J. · 1 citation
#05C15 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1201.0486

Abstract

Let G be the graph with the points of the unit sphere in ℝ³ 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.

Cited by

• Vector Trifference

Related

• Coloring spheres in 3--manifolds
• Four plane unit vectors generate a 3-colorable graph
• Graphs with Eulerian unit spheres
• Chromatic numbers of spheres
• The surface of a sufficiently large sphere has chromatic number at most\n 7