Stationary map coloring

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)327-342
Number of pages16
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume48
Issue number2
DOIs
StatePublished - May 2012

Keywords

  • Delaunay triangulation
  • Graph coloring
  • Percolation
  • Planar graphs
  • Poisson process
  • Voronoi tessellation

Fingerprint

Dive into the research topics of 'Stationary map coloring'. Together they form a unique fingerprint.

Cite this