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Diagonal Flips of Triangulations on Closed Surfaces Preserving Specified Properties

✍ Scribed by Richard Brunet; Atsuhiro Nakamoto; Seiya Negami

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 445 KB
Volume: 68
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0070

No coin nor oath required. For personal study only.

✦ Synopsis

Consider a class P of triangulations on a closed surface F 2 , closed under vertex splitting. We shall show that any two triangulations with the same and sufficiently large number of vertices which belong to P can be transformed into each other, up to homeomorphism, by a finite sequence of diagonal flips through P. Moreover, if P is closed under homeomorphism, then the condition up to homeomorphism'' can be replaced with up to isotopy.''

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✍ Hideo Komuro; Atsuhiro Nakamoto; Seiya Negami 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 365 KB

It will be shown that any two triangulations on a closed surface, except the sphere, with minimum degree at least 4 can be transformed into each other by a finite sequence of diagonal flips through those triangulations if they have a sufficiently large and same number of vertices. The same fact hold