Stationary map coloring

Omer Angel; Itai Benjamini; Ori Gurel-Gurevich; Tom Meyerovitch; Ron Peled

doi:10.1214/10-AIHP399

Stationary map coloring

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

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	327-342
Number of pages	16
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	48
Issue number	2
DOIs	https://doi.org/10.1214/10-AIHP399
State	Published - May 2012
Externally published	Yes

Keywords

Delaunay triangulation
Graph coloring
Percolation
Planar graphs
Poisson process
Voronoi tessellation

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10.1214/10-AIHP399

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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.",

keywords = "Delaunay triangulation, Graph coloring, Percolation, Planar graphs, Poisson process, Voronoi tessellation",

author = "Omer Angel and Itai Benjamini and Ori Gurel-Gurevich and Tom Meyerovitch and Ron Peled",

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AU - Meyerovitch, Tom

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KW - Delaunay triangulation

KW - Graph coloring

KW - Percolation

KW - Planar graphs

KW - Poisson process

KW - Voronoi tessellation

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Stationary map coloring

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Keywords

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