Steiner minimal trees for regular polygons
type: Item
instance of: scholarly article
title: Steiner minimal trees for regular polygons
zbMATH Open document ID: 0607.05022
DOI: 10.1007/BF02187871
author: B. George
published in: Discrete \& Computational Geometry
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131010
review text: 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.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 3981189
zbMATH Keywords: Steiner minimal tree
reviewed by: Alan C. Tucker
MaRDI profile type: Publication
cites work: Steiner Trees for Ladders
cites work: Q3689203
cites work: A New Bound for the Steiner Ratio
cites work: Steiner minimal trees for bar waves
cites work: Steiner Minimal Trees on Zig-Zag Lines
cites work: Steiner Minimal Tree for Points on a Circle
cites work: The Complexity of Computing Steiner Minimal Trees
cites work: Fuzzy sets
cites work: A class of full Steiner minimal trees
cites work: On the Problem of Steiner
cites work: Hexagonal coordinate systems and Steiner minimal trees
OpenAlex ID: W2090486508
description: scientific article; zbMATH DE number 3981189