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The Voronoi Functional is Maximized by the Delaunay Triangulation in the Plane (1411.6337v1)
Published 24 Nov 2014 in math.MG and math.CO
Abstract: We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.