This article is cited in 2 papers

The Structure of Minimal Steiner Trees in the Neighborhoods of the Lunes of Their Edges

A. O. Ivanov^ab, O. A. S'edina^a, A. A. Tuzhilin<sup>ab

a</sup> M. V. Lomonosov Moscow State University
^b P. G. Demidov Yaroslavl State University

Abstract: We give a complete description of small neighborhoods of the closures of lunes of the edges of Steiner minimal trees (Theorem 1.1); to this end, we prove a generalization of a stabilization theorem for embedded locally minimal trees [1]; the case of two such disjoint trees is considered (Theorem 2.2).

Keywords: Steiner minimal tree, locally minimal tree, lune of an edge of a tree, linear graph, shortest tree.

UDC: 514.774.8+519.176

Received: 08.07.2009
Revised: 25.03.2011

DOI: 10.4213/mzm8533

 English version: Mathematical Notes, 2012, 91:3, 339–353

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