Stationary map coloring
Omer Angel, Itai Benjamini, Ori Gurel-Gurevich, Tom Meyerovitch, Ron, Peled

TL;DR
This paper proves that a planar Voronoi map derived from a Poisson process can be properly colored with 6 colors in a deterministic, isometry-equivariant way, and explores related geometric properties and open questions.
Contribution
It establishes the existence of a 6-coloring for the Voronoi map as a deterministic, isometry-equivariant function of the Poisson process, and analyzes the Delaunay triangulation core.
Findings
Existence of a 6-coloring for the Voronoi map.
The 6-core of the Delaunay triangulation is empty.
Discussion of generalizations and open questions.
Abstract
We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant function of the Poisson process. As part of the proof we show that the 6-core of the corresponding Delaunay triangulation is empty. Generalizations, extensions and some open questions are discussed.
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Taxonomy
TopicsPoint processes and geometric inequalities · Computational Geometry and Mesh Generation · Advanced Combinatorial Mathematics
