Witness Gabriel Graphs

@article{Aronov2009WitnessGG,
  title={Witness Gabriel Graphs},
  author={Boris Aronov and Muriel Dulieu and Ferran Hurtado},
  journal={Comput. Geom.},
  year={2009},
  volume={46},
  pages={894-908}
}
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. 

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