RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb., 2006, Volume 197, Number 9, Pages 55–90 (Mi msb1463)

Uniqueness of Steiner minimal trees on boundaries in general position

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The following result is proved: there exists an open dense subset $U$ of $\mathbb R^{2n}$ such that each $P\in U$ (regarded as an enumerated subset of the standard Euclidean plane $\mathbb R^2$) is spanned by a unique Steiner minimal tree, that is, a shortest non-degenerate network. Several interesting consequences are also obtained: in particular, it is proved that each planar Steiner tree is planar equivalent to a Steiner minimal tree.
Bibliography: 11 titles.

DOI: https://doi.org/10.4213/sm1463

Full text: PDF file (813 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:9, 1309–1340

Bibliographic databases:

UDC: 514.774.8+519.176
MSC: Primary 7M15; Secondary 05C05

Citation: A. O. Ivanov, A. A. Tuzhilin, “Uniqueness of Steiner minimal trees on boundaries in general position”, Mat. Sb., 197:9 (2006), 55–90; Sb. Math., 197:9 (2006), 1309–1340

Citation in format AMSBIB
\Bibitem{IvaTuz06} \by A.~O.~Ivanov, A.~A.~Tuzhilin \paper Uniqueness of Steiner minimal trees on boundaries in general position \jour Mat. Sb. \yr 2006 \vol 197 \issue 9 \pages 55--90 \mathnet{http://mi.mathnet.ru/msb1463} \crossref{https://doi.org/10.4213/sm1463} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2273168} \zmath{https://zbmath.org/?q=an:1168.05304} \elib{https://elibrary.ru/item.asp?id=9277053} \transl \jour Sb. Math. \yr 2006 \vol 197 \issue 9 \pages 1309--1340 \crossref{https://doi.org/10.1070/SM2006v197n09ABEH003800} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243495000004} \elib{https://elibrary.ru/item.asp?id=18101778} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846523648} 

• http://mi.mathnet.ru/eng/msb1463
• https://doi.org/10.4213/sm1463
• http://mi.mathnet.ru/eng/msb/v197/i9/p55

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Oblakov K.I., “Non-existence of distinct codirected locally minimal trees on a plane”, Moscow Univ. Math. Bull., 64:2 (2009), 62–66
2. H. Edelsbrunner, N. P. Strelkova, “On the configuration space of Steiner minimal trees”, Russian Math. Surveys, 67:6 (2012), 1167–1168
3. H. Edelsbrunner, A. Ivanov, R. Karasev, “Current Open Problems in Discrete and Computational Geometry”, Model. i analiz inform. sistem, 19:5 (2012), 5–17
4. Zachos A.N., “An Evolutionary Structure of Convex Pentagons on a C-2 Complete Surface and a Creation Principle of Some Weighted Dendrites of Order Three”, J. Convex Anal., 20:4 (2013), 1043–1073
5. “Minimal Fillings of Finite Metric Spaces: the State of the Art”, Discrete Geometry and Algebraic Combinatorics, Contemporary Mathematics, 625, 2014, 9+
6. 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
•  Number of views: This page: 566 Full text: 195 References: 31 First page: 6