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Stationary map coloring

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arxiv 0905.2563 v1 pith:LC2DDGCI submitted 2009-05-15 math.PR math.CO

Omer Angel , Itai Benjamini , Ori Gurel-Gurevich , Tom Meyerovitch , Ron Peled This is my paper · ORCID
classification math.PRmath.CO
keywords coloringpoissonprocessassociatedcolorsconsidercorecorresponding
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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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