### 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, 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 |
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Pages | 13-16 |

Number of pages | 4 |

Publication status | Published - 2010 Dec 1 |

Externally published | Yes |

Event | 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010 - Winnipeg, MB, Canada Duration: 2010 Aug 9 → 2010 Aug 11 |

### Other

Other | 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010 |
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Country | Canada |

City | Winnipeg, MB |

Period | 10/8/9 → 10/8/11 |

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology

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## Cite this

Bose, P., Collette, S., Hurtado, F., Korman, M., Langerman, S., Sacristán, V., & Saumell, M. (2010).

*Some properties of higher order delaunay and gabriel graphs*. 13-16. Paper presented at 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, Winnipeg, MB, Canada.