Published on *Computer Science Department at Princeton University* (https://www.cs.princeton.edu)

Let S be any set of N points in the plane and let DT(S) be the graph of the Delaunay triangulation of S. For all points a and b of S, let d(a,b) be the Euclidean distance from a to b and let DT(a,b) be the length of the shortest path in DT(S) from a to b. We show that there is a constant c(leq {1+sqrt5}/2)x pi approx 5.08)independent of S and N such that DT(a,b)/d(a,b) less than c.

**Links**

[1] https://www.cs.princeton.edu/research/techreps/author/375

[2] https://www.cs.princeton.edu/research/techreps/author/49

[3] https://www.cs.princeton.edu/research/techreps/author/469

[4] ftp://ftp.cs.princeton.edu/techreports/1987/113.pdf