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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@inproceedings{Angel2009StationaryMC, title={Stationary map coloring}, author={Omer Angel and Itai Benjamini and Ori Gurel-Gurevich and Tom Meyerovitch and Ron Peled}, year={2009} }