The Steiner ratio conjecture for cocircular points

Abstract

A Steiner minimal treeS is a network of shortest possible length connecting a set ofn points in the plane. LetT be a shortest tree connecting then points but with vertices only at these points.T is called a minimal spanning tree. The Steiner ratio conjecture is that the length ofS divided by the length ofT is at least √3/2. In this paper we use a variational approach to show that if then points lie on a circle, then the Steiner ratio conjecture holds.