论文信息 - Steiner minimal trees for regular polygons

Steiner minimal trees for regular polygons

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.

Ding-Zhu Du | Frank K. Hwang | J. F. Weng

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