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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)
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2008, Volume 72, Issue 1, Pages 67–98
DOI: https://doi.org/10.4213/im534
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. RAN. Ser. Mat., 72:1 (2008), 67–98; Izv. Math., 72:1 (2008), 63–90
Citation in format AMSBIB
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    • 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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    Russian version PDF:367
    English version PDF:19
    References:64
    First page:14
     
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