The odd-distance plane graph

Hayri Ardal, Ján Maňuch, Moshe Rosenfeld*, Saharon Shelah, Ladislav Stacho

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The vertices of the odd-distance graph are the points of the plane ℝ2. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chromatic number of this graph is at least five. We also prove that the odd-distance graph in ℝ2 is countably choosable, while such a graph in ℝ3 is not.

Original languageEnglish
Pages (from-to)132-141
Number of pages10
JournalDiscrete and Computational Geometry
Volume42
Issue number2
DOIs
StatePublished - Sep 2009

Keywords

  • Graph coloring
  • List-chromatic number (choosability)
  • The unit-distance graph

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