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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 1, Pages 67–98 (Mi izv534)  

This article is cited in 4 scientific papers (total in 4 papers)

Immersed polygons and their diagonal triangulations

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We introduce the notion of an ‘immersed polygon’, which naturally extends the notion of an ordinary planar polygon bounded by a closed (embedded) polygonal arc to the case when this arc may have self-intersections. We prove that every immersed polygon admits a diagonal triangulation and the closure of every embedded monotone polygonal arc bounds an immersed polygon. Given any non-degenerate planar linear tree, we construct an immersed polygon containing it.

DOI: https://doi.org/10.4213/im534

Full text: PDF file (718 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:1, 63–90

Bibliographic databases:

UDC: 514.77+512.816.4+517.924.8
MSC: 05C05, 51M16, 53C42
Received: 28.02.2005

Citation: A. O. Ivanov, A. A. Tuzhilin, “Immersed polygons and their diagonal triangulations”, Izv. RAN. Ser. Mat., 72:1 (2008), 67–98; Izv. Math., 72:1 (2008), 63–90

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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. I. S. Mekhedov, “A multisheet plane figure and its medial axis”, Russian Math. (Iz. VUZ), 55:12 (2011), 34–43  mathnet  crossref  mathscinet
    2. Ivanov A.O., Tuzhilin A.A., “The Steiner ratio Gilbert–Pollak conjecture is still open”, Algorithmica, 62:1-2 (2012), 630–632  crossref  mathscinet  zmath  isi  scopus
    3. A. O. Ivanov, A. A. Tuzhilin, “The geometry of inner spanning trees for planar polygons”, Izv. Math., 76:2 (2012), 215–244  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Naya Sh., Innami N., “A Comparison Theorem for Steiner Minimum Trees in Surfaces with Curvature Bounded Below”, Tohoku Math. J., 65:1 (2013), 131–157  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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