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 | |
| Publication status | Published - 2013 Feb 1 |
| Externally published | Yes |
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