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Izvestiya: Mathematics, 2008, Volume 72, Issue 1, Pages 63–90
DOI: https://doi.org/10.1070/IM2008v072n01ABEH002392 (Mi im534) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Immersed polygons and their diagonal triangulations

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (415 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/IM2008v072n01ABEH002392
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.
Received: 28.02.2005
Bibliographic databases:
UDC: 514.77+512.816.4+517.924.8
MSC: 05C05, 51M16, 53C42
Language: English
Original paper language: Russian
Citation: A. O. Ivanov, A. A. Tuzhilin, “Immersed polygons and their diagonal triangulations”, Izv. Math., 72:1 (2008), 63–90
Citation in format AMSBIB
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\paper Immersed polygons and their diagonal triangulations
\jour Izv. Math.
\yr 2008
\vol 72
\issue 1
\pages 63--90
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  • https://doi.org/10.1070/IM2008v072n01ABEH002392
  • https://www.mathnet.ru/eng/im/v72/i1/p67
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:747
    Russian version PDF:382
    English version PDF:27
    References:76
    First page:14
     
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