Some properties of k-Delaunay and k-Gabriel graphs

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

doi:10.1016/j.comgeo.2012.04.006

Some properties of k-Delaunay and k-Gabriel graphs

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

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	131-139
Number of pages	9
Journal	Computational Geometry: Theory and Applications
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/j.comgeo.2012.04.006
Publication status	Published - 2013 Feb

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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10.1016/j.comgeo.2012.04.006

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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.",

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AU - Hurtado, Ferran

AU - Korman, Matias

AU - Langerman, Stefan

AU - Sacristán, Vera

AU - Saumell, Maria

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AB - 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.

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KW - Proximity graphs

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ER -

Some properties of k-Delaunay and k-Gabriel graphs

Abstract

Keywords

ASJC Scopus subject areas

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