### Abstract

We consider a generalization of the Gabriel graph, the witness Gabriel graph. Given a set of vertices P and a set of witness points W in the plane, there is an edge ab between two points of P in the witness Gabriel graph ^{GG-}(P,W) if and only if the closed disk with diameter ab does not contain any witness point (besides possibly a and/or b). We study several properties of the witness Gabriel graph, both as a proximity graph and as a new tool in graph drawing.

Original language | English (US) |
---|---|

Pages (from-to) | 894-908 |

Number of pages | 15 |

Journal | Computational Geometry: Theory and Applications |

Volume | 46 |

Issue number | 7 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### Keywords

- Gabriel graph
- Graph drawing
- Proximity graph
- Witness graph

### ASJC Scopus subject areas

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

### Cite this

*Computational Geometry: Theory and Applications*,

*46*(7), 894-908. https://doi.org/10.1016/j.comgeo.2011.06.004

**Witness Gabriel graphs.** / Aronov, Boris; Dulieu, Muriel; Hurtado, Ferran.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 46, no. 7, pp. 894-908. https://doi.org/10.1016/j.comgeo.2011.06.004

}

TY - JOUR

T1 - Witness Gabriel graphs

AU - Aronov, Boris

AU - Dulieu, Muriel

AU - Hurtado, Ferran

PY - 2013

Y1 - 2013

N2 - We consider a generalization of the Gabriel graph, the witness Gabriel graph. Given a set of vertices P and a set of witness points W in the plane, there is an edge ab between two points of P in the witness Gabriel graph GG-(P,W) if and only if the closed disk with diameter ab does not contain any witness point (besides possibly a and/or b). We study several properties of the witness Gabriel graph, both as a proximity graph and as a new tool in graph drawing.

AB - We consider a generalization of the Gabriel graph, the witness Gabriel graph. Given a set of vertices P and a set of witness points W in the plane, there is an edge ab between two points of P in the witness Gabriel graph GG-(P,W) if and only if the closed disk with diameter ab does not contain any witness point (besides possibly a and/or b). We study several properties of the witness Gabriel graph, both as a proximity graph and as a new tool in graph drawing.

KW - Gabriel graph

KW - Graph drawing

KW - Proximity graph

KW - Witness graph

UR - http://www.scopus.com/inward/record.url?scp=84878535127&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878535127&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2011.06.004

DO - 10.1016/j.comgeo.2011.06.004

M3 - Article

VL - 46

SP - 894

EP - 908

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 7

ER -