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


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.


Unit Circle Minimal Span Tree Discrete Comput Geom Steiner Tree Regular Point 
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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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