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10 Excerpts

@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} }

- Published in Comput. Geom. 2009
DOI:10.1016/j.comgeo.2011.06.004

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.