Note on the chromatic number of Minkowski planes: the regular polygon case

2023/01/31 by Panna Gehér, Gehér, Panna · 1 citation
Psychology · #Color perception and design #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2301.13695

openalex publication_date 2023/01/31 · openalex created_date 2023/02/03 · openalex updated_date 2026/07/28

Abstract

The famous Hadwiger-Nelson problem asks for the minimum number of colors needed to color the points of the Euclidean plane so that no two points unit distance apart are assigned the same color. In this note we consider a variant of the problem in Minkowski metric planes, where the unit circle is a regular polygon of even and at most 22 vertices. We present a simple lattice-sublattice coloring scheme that uses 6 colors, proving that the chromatic number of the Minkowski planes above are at most 6. This result is new for regular polygons having more than 8 vertices.

Cited by

• Ramsey problems for graphs in Euclidean spaces and Cartesian powers

Related

• The chromatic number of the Minkowski plane -- the regular polygon case
• The chromatic number of the plane with an interval of forbidden distances is at least 7
• On the chromatic number of the plane for map-type colorings
• The chromatic number of the plane is at least 5
• Triangle colorings require at least seven colors