The Steiner ratio conjecture for cocircular points

Abstract

A Steiner minimal tree S is a network of shortest possible length connecting a set of n points in the plane. Let T be a shortest tree connecting the n points but with vertices only at these points. T is called a minimal spanning tree. The Steiner ratio conjecture is that the length of S divided by the length of T is at least √3/2. In this paper we use a variational approach to show that if the n points lie on a circle, then the Steiner ratio conjecture holds. © 1992 Springer-Verlag New York Inc.