Some properties of k-Delaunay and k-Gabriel graphs

Prosenjit Bose, Sébastien Collette, Ferran Hurtado, Matias Korman, Stefan Langerman, Vera Sacristán, Maria Saumell

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the following combinatorial and geometric properties of these graphs: spanning ratio, diameter, connectivity, chromatic number, and minimum number of layers necessary to partition the edges of the graphs so that no two edges of the same layer cross.

Original languageEnglish
Pages (from-to)131-139
Number of pages9
JournalComputational Geometry: Theory and Applications
Volume46
Issue number2
DOIs
Publication statusPublished - 2013 Feb 1
Externally publishedYes

Keywords

  • Geometric graphs
  • Proximity graphs

ASJC Scopus subject areas

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

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  • Cite this

    Bose, P., Collette, S., Hurtado, F., Korman, M., Langerman, S., Sacristán, V., & Saumell, M. (2013). Some properties of k-Delaunay and k-Gabriel graphs. Computational Geometry: Theory and Applications, 46(2), 131-139. https://doi.org/10.1016/j.comgeo.2012.04.006