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Discrete & Computational Geometry

, Volume 2, Issue 1, pp 65–84 | Cite as

Steiner minimal trees for regular polygons

  • D. Z. Du
  • F. K. Hwang
  • J. F. Weng
Article

Abstract

Fifty years ago Jarnik and Kössler showed that a Steiner minimal tree for the vertices of a regularn-gon contains Steiner points for 3 ≤n≤5 and contains no Steiner point forn=6 andn≥13. We complete the story by showing that the case for 7≤n≤12 is the same asn≥13. We also show that the set ofn equally spaced points yields the longest Steiner minimal tree among all sets ofn cocircular points on a given circle.

Keywords

Unit Circle Minimal Span Tree Discrete Comput Geom Steiner Tree Regular Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • D. Z. Du
    • 1
    • 2
  • F. K. Hwang
    • 3
  • J. F. Weng
    • 4
  1. 1.University of CaliforniaSanta BarbaraUSA
  2. 2.Academia SinicaBeijingChina
  3. 3.AT&T Bell LaboratoriesMurray HillUSA
  4. 4.Baoshan General Iron and Steel WorksShanghaiChina

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