On the hyperbolicity of Delaunay triangulations

If is a geodesic metric space and , a geodesic triangle is the union of the three geodesics, and in. The space is hyperbolic if there exists a constant such that any side of any geodesic triangle in is contained in the -neighborhood of the union of the two other sides. In this paper, we study the hyperbolicity of an important kind of Euclidean graphs called Delaunay triangulations. Furthermore, we characterize the Delaunay triangulations contained in the Euclidean plane that are hyperbolic.

On the hyperbolicity of Delaunay triangulations Articles