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Sbornik: Mathematics, 2017, Volume 208, Issue 4, Pages 479–509
DOI: https://doi.org/10.1070/SM8746 (Mi sm8746) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Extremal networks in $\lambda$-geometry, where $\lambda=3,4,6$

D. P. Ilyutko, I. M. Nikonov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (1039 kB) Citations (2)
References:
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DOI: https://doi.org/10.1070/SM8746
Abstract: The first author obtained a geometric criterion for a network to be extremal in $\lambda$-geometry for $\lambda\ne2,3,4,6$. The case $\lambda=2$ was examined by Ivanov and Tuzhilin. In this work, we suggest an extremality criterion for the remaining three cases $\lambda=3,4,6$.
Bibliography: 21 titles.
Keywords: Steiner tree problem, normed plane, network, locally minimal network, extremal network.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00378-a
Ministry of Education and Science of the Russian Federation НШ-7962.2016.1
This work was supported by the Russian Foundation for Basic Research (grant no. 16-01-00378_a) and by the Council of the President of the Russian Federation for the State Support of Leading Scientific Schools (grant no. НШ-7962.2016.1).
Received: 26.05.2016 and 21.01.2017
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 4, Pages 17–50
DOI: https://doi.org/10.4213/sm8746
Bibliographic databases:
Document Type: Article
UDC: 514.77+517.972/.974+519.17
MSC: Primary 05C35; Secondary 05C05, 46B20, 90C35
Language: English
Original paper language: Russian
Citation: D. P. Ilyutko, I. M. Nikonov, “Extremal networks in $\lambda$-geometry, where $\lambda=3,4,6$”, Mat. Sb., 208:4 (2017), 17–50; Sb. Math., 208:4 (2017), 479–509
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    References:39
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