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Mat. Sb., 1999, Volume 190, Number 1, Pages 69–108 (Mi msb378)  

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

Geometry of convex polygons and locally minimal binary trees spanning these polygons

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University

Abstract: In previous works the authors have obtained an effective classification of planar locally minimal binary trees with convex boundaries. The main aim of the present paper is to find more subtle restrictions on the possible structure of such trees in terms of the geometry of the given boundary set. Special attention is given to the case of quasiregular boundaries (that is, boundaries that are sufficiently close to regular ones in a certain sense). In particular, a series of quasiregular boundaries that cannot be spanned by a locally minimal binary tree is constructed.

DOI: https://doi.org/10.4213/sm378

Full text: PDF file (478 kB)
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English version:
Sbornik: Mathematics, 1999, 190:1, 71–110

Bibliographic databases:

UDC: 514.77+512.816.4+517.924.8
MSC: 05C35
Received: 27.01.1998

Citation: A. O. Ivanov, A. A. Tuzhilin, “Geometry of convex polygons and locally minimal binary trees spanning these polygons”, Mat. Sb., 190:1 (1999), 69–108; Sb. Math., 190:1 (1999), 71–110

Citation in format AMSBIB
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\paper Geometry of convex polygons and locally minimal binary trees spanning these polygons
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\yr 1999
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\issue 1
\pages 69--108
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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. Ivanov, AO, “Extreme networks”, Acta Applicandae Mathematicae, 66:3 (2001), 251  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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