Stationary map coloring

Details Stationary map coloring Stationary map coloring

2009-05-15

arxiv.org/abs/0905.2563v1

Mathematics

Probability

21 pages, 1 figure

Scientific paper

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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