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Mat. Zametki, 2012, Volume 91, Issue 3, Pages 353–370 (Mi mz8533)  

This article is cited in 2 scientific papers (total in 2 papers)

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

A. O. Ivanovab, O. A. S'edinaa, A. A. Tuzhilinab

a 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

DOI: https://doi.org/10.4213/mzm8533

Full text: PDF file (673 kB)
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English version:
Mathematical Notes, 2012, 91:3, 339–353

Bibliographic databases:

UDC: 514.774.8+519.176
Received: 08.07.2009
Revised: 25.03.2011

Citation: A. O. Ivanov, O. A. S'edina, A. A. Tuzhilin, “The Structure of Minimal Steiner Trees in the Neighborhoods of the Lunes of Their Edges”, Mat. Zametki, 91:3 (2012), 353–370; Math. Notes, 91:3 (2012), 339–353

Citation in format AMSBIB
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\pages 353--370
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  • https://doi.org/10.4213/mzm8533
  • http://mi.mathnet.ru/eng/mz/v91/i3/p353

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    This publication is cited in the following articles:
    1. A. O. Ivanov, A. E. Mel'nikova, A. A. Tuzhilin, “Stabilization of a locally minimal forest”, Sb. Math., 205:3 (2014), 387–418  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Ivanov A.O. Tuzhilin A.A., “Minimal Networks: a Review”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, ed. Sadovnichiy V. Zgurovsky M., Springer Int Publishing Ag, 2016, 43–80  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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