Steiner minimal trees for regular polygons
A Steiner minimal tree for a set of points P in the plane is a shortest network interconnecting P. This paper shows that for the vertices of a regular n-gon, \(7\leq n\leq 12\), the Steiner minimal tree consists of the perimeter of the regular n-gon minus one side (this result had previously been proved for \(n\geq 13)\). It is also shown that the set of n equally spaced points yields the longest Steiner minimal tree among all sets of n cocircular points on a given circle.
scientific article; zbMATH DE number 3981189
scientific article