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Mat. Sb., 1996, Volume 187, Number 8, Pages 41–92 (Mi msb151)  

This article is cited in 7 scientific papers (total in 7 papers)

The twist number of planar linear trees

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University

Abstract: New natural geometric characteristics are introduced for planar linear trees: the boundary set and the twist number. It turns out that the number of convexity levels of the boundary set is bounded above by a linear function of the twist number. As consequences of this general fact, some non-trivial assertions are obtained about the geometry of linear trees that are extremals of the length or weight functional.

DOI: https://doi.org/10.4213/sm151

Full text: PDF file (544 kB)
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English version:
Sbornik: Mathematics, 1996, 187:8, 1149–1195

Bibliographic databases:

UDC: 514.77
MSC: Primary 05C05, 05C35; Secondary 05C90, 90C35
Received: 15.11.1995

Citation: A. O. Ivanov, A. A. Tuzhilin, “The twist number of planar linear trees”, Mat. Sb., 187:8 (1996), 41–92; Sb. Math., 187:8 (1996), 1149–1195

Citation in format AMSBIB
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\paper The twist number of planar linear trees
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\yr 1996
\vol 187
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\pages 41--92
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\issue 8
\pages 1149--1195
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    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. A. O. Ivanov, A. A. Tuzhilin, “The geometry of minimal networks with a given topology and a fixed boundary”, Izv. Math., 61:6 (1997), 1231–1263  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. O. Ivanov, A. A. Tuzhilin, “The space of parallel linear networks with a fixed boundary”, Izv. Math., 63:5 (1999), 923–962  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Ivanov, AO, “Extreme networks”, Acta Applicandae Mathematicae, 66:3 (2001), 251  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Ivanov, AO, “Planar Manhattan local minimal and critical networks”, European Journal of Combinatorics, 23:8 (2002), 949  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. N. S. Gusev, “Convex Realizations of Planar Linear Trees”, Math. Notes, 73:5 (2003), 625–635  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  scopus
    7. I. L. Laut, “Correlation between the norm and the geometry of minimal networks”, Sb. Math., 208:5 (2017), 684–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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