On the stretch factor of convex delaunay graphs
Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q.
Bose, P, Carmi, P. (Paz), Collette, S. (Sébastien), & Smid, M. (2008). On the stretch factor of convex delaunay graphs. doi:10.1007/978-3-540-92182-0_58