This article is cited in 4 papers

Stabilization of Locally Minimal Trees

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: It is proved that any locally minimal tree on Euclidean space can be “stabilized” (i.e., rendered shortest) by adding boundary vertices without changing the initial tree as a set in space. This result is useful for constructing examples of shortest trees.

Keywords: Steiner's problem, Steiner minimal tree, shortest tree, shortest network, framed network, Euclidean network, stabilization of a network.

UDC: 514.774.8+519.176

Received: 25.07.2007
Revised: 26.09.2008

DOI: 10.4213/mzm4023

 English version: Mathematical Notes, 2009, 86:4, 483–492

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