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Mat. Sb., 2017, Volume 208, Number 4, Pages 17–50 (Mi msb8746)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8746

Full text: PDF file (1199 kB)
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English version:
Sbornik: Mathematics, 2017, 208:4, 479–509

Bibliographic databases:

UDC: 514.77+517.972/.974+519.17
MSC: Primary 05C35; Secondary 05C05, 46B20, 90C35
Received: 26.05.2016 and 21.01.2017

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Yu. Zhitnaya, “Modelirovanie optimalnykh setei s pomoschyu sharnirnykh mekhanizmov”, Fundament. i prikl. matem., 22:6 (2019), 95–122  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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