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Matematicheskie Zametki, 2012, Volume 91, Issue 3, Pages 353–370
DOI: https://doi.org/10.4213/mzm8533 (Mi mzm8533) 		 
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
Full-text PDF (673 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm8533
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.
Received: 08.07.2009
Revised: 25.03.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 3, Pages 339–353
DOI: https://doi.org/10.1134/S0001434612030042
Bibliographic databases:
Document Type: Article
UDC: 514.774.8+519.176
Language: Russian
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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\vol 91
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\pages 353--370
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  • https://www.mathnet.ru/eng/mzm8533
  • https://doi.org/10.4213/mzm8533
  • https://www.mathnet.ru/eng/mzm/v91/i3/p353
    • This publication is cited in the following 2 articles:
    1. 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
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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