Discrete & Computational Geometry

, Volume 7, Issue 1, pp 77–86 | Cite as

The Steiner ratio conjecture for cocircular points

  • J. H. Rubinstein
  • D. A. Thomas
Article

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.

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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • J. H. Rubinstein
    • 1
    • 2
  • D. A. Thomas
    • 2
  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsUniversity of MelbourneParkvilleAustralia

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