Measurable Chromatic Number of Spheres

2014/12/05 by Greg Malen, Malen, Greg
Computer Science · Materials Science · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1412.2091

openalex publication_date 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the measurable chromatic number of distance colorings on the surface of 2-dimensional spheres of varying radii, showing in particular that similar arguments to those used to raise lower bounds in the plane work for all but a countable set of radii. Furthermore, we show that measurable chromatic number as a function of the radius, or more generally the curvature, is not monotonic.

Citations

• Coloring distance graphs: a few answers and many questions

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