This article is cited 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

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.

UDC: 514.77+517.972/.974+519.17

MSC: Primary 05C35; Secondary 05C05, 46B20, 90C35

Received: 26.05.2016 and 21.01.2017

DOI: 10.4213/sm8746

 English version: Sbornik: Mathematics, 2017, 208:4, 479–509

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