Geometric spanners with small chromatic number

Prosenjit Bose, Paz Carmi, Mathieu Couture, Anil Maheshwari, Michiel Smid, Norbert Zeh

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Given an integer k≥2, we consider the problem of computing the smallest real number t(k) such that for each set P of points in the plane, there exists a t(k)-spanner for P that has chromatic number at most k. We prove that t(2)=3, t(3)=2, t(4)=2, and give upper and lower bounds on t(k) for k>4. We also show that for any >0, there exists a (1+)t(k)-spanner for P that has O(|P|) edges and chromatic number at most k. Finally, we consider an on-line variant of the problem where the points of P are given one after another, and the color of a point must be assigned at the moment the point is given. In this setting, we prove that t(2)=3, t(3)=1+3, t(4)=1+2, and give upper and lower bounds on t(k) for k>4.

Original languageEnglish
Pages (from-to)134-146
Number of pages13
JournalComputational Geometry: Theory and Applications
Issue number2
StatePublished - 1 Feb 2009
Externally publishedYes


  • Computational geometry
  • Geometric graph
  • Online algorithm
  • Paz graph
  • Spanners
  • k-colorable graphs

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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