Some properties of k-Delaunay and k-Gabriel graphs

Authors:
Prosenjit Bose;SéBastien Collette;Ferran Hurtado;Matias Korman;Stefan Langerman;Vera SacristáN;Maria Saumell
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada;Computer Science Department, Université Libre de Bruxelles, Brussels, Belgium;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Computer Science Department, Université Libre de Bruxelles, Brussels, Belgium;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Department of Applied Mathematics, Charles University, Prague, Czech Republic
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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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.