Discrete & Computational Geometry

, Volume 9, Issue 3, pp 323–333 | Cite as

The steiner minimal network for convex configurations

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

Abstract

SupposeX is a convex configuration with radius of maximum curvaturer and at most one of the edges joining neighboring points has length strictly greater thanr. We use the variational approach to show the Steiner treeS coincides with the minimal spanning tree and consists of all these edges with a longest edge removed. This generalizes Graham's problem for points on a circle, which we had solved. In addition we describe the minimal spanning tree for certain convex configurations.

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References

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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • D. A. Thomas
    • 1
  • J. H. Rubinstein
    • 1
  • T. Cole
    • 1
  1. 1.Mathematics DepartmentMelbourne UniversityParkvilleAustralia

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