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

Tel Aviv University, Weizmann Institute of Science

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

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 - 1 May 2012

Keywords

Delaunay triangulation
Graph coloring
Percolation
Planar graphs
Poisson process
Voronoi tessellation

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/10-AIHP399

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title = "Stationary map coloring",

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",

note = "NSERC; NSF [OISE 0730136]Research supported by NSERC.Partially completed during stay at the Institut Henri Poincare - Centre Emile Borel. Research supported by NSF Grant OISE 0730136.",

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doi = "10.1214/10-AIHP399",

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T1 - Stationary map coloring

AU - Angel, Omer

AU - Benjamini, Itai

AU - Gurel-Gurevich, Ori

AU - Meyerovitch, Tom

AU - Peled, Ron

N1 - NSERC; NSF [OISE 0730136]Research supported by NSERC.Partially completed during stay at the Institut Henri Poincare - Centre Emile Borel. Research supported by NSF Grant OISE 0730136.

PY - 2012/5/1

Y1 - 2012/5/1

N2 - 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.

AB - 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.

KW - Delaunay triangulation

KW - Graph coloring

KW - Percolation

KW - Planar graphs

KW - Poisson process

KW - Voronoi tessellation

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U2 - 10.1214/10-AIHP399

DO - 10.1214/10-AIHP399

M3 - مقالة

SN - 0246-0203

VL - 48

SP - 327

EP - 342

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 2

ER -

Stationary map coloring

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Keywords

All Science Journal Classification (ASJC) codes

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