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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
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
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
Linking options:
https://www.mathnet.ru/eng/im534https://doi.org/10.1070/IM2008v072n01ABEH002392 https://www.mathnet.ru/eng/im/v72/i1/p67
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Abstract page: | 709 | Russian version PDF: | 367 | English version PDF: | 19 | References: | 64 | First page: | 14 |
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