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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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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