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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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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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