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Matematicheskie Zametki, 2009, Volume 86, Issue 4, Pages 512–524
DOI: https://doi.org/10.4213/mzm4023 (Mi mzm4023) 		 
This article is cited in 4 scientific papers (total 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
Full-text PDF (480 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm4023
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.
Received: 25.07.2007
Revised: 26.09.2008
English version:
Mathematical Notes, 2009, Volume 86, Issue 4, Pages 483–492
DOI: https://doi.org/10.1134/S0001434609090247
Bibliographic databases:
UDC: 514.774.8+519.176
Language: Russian
Citation: A. O. Ivanov, A. A. Tuzhilin, “Stabilization of Locally Minimal Trees”, Mat. Zametki, 86:4 (2009), 512–524; Math. Notes, 86:4 (2009), 483–492
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm4023
  • https://doi.org/10.4213/mzm4023
  • https://www.mathnet.ru/eng/mzm/v86/i4/p512
    • This publication is cited in the following 4 articles:
    1. I. L. Laut, “Correlation between the norm and the geometry of minimal networks”, Sb. Math., 208:5 (2017), 684–706  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
    3. 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
    4. 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”, Math. Notes, 91:3 (2012), 339–353  mathnet  crossref  crossref  mathscinet  isi  elib  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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    References:55
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