Diagonal flips in triangulations of surfaces
type: Item
instance of: scholarly article
title: Diagonal flips in triangulations of surfaces
zbMATH Open document ID: 0823.05028
DOI: 10.1016/0012-365X(93)E0101-9
author: Seiya Negami
published in: Discrete Mathematics
publication date: 1995-02-01T00:00:00Z
review text: A triangulation \(G\) of a closed surface \(\text{F}^ 2\) is a simple graph, without loops and multiple edges, which is embedded on \(\text{F}^ 3\) so that each face is triangular and so that any two faces meet along at most one edge. Let \(abc\) and \(acd\) be two triangular faces of \(G\) which have an edge \(ac\) in common. The diagonal flip of \(ac\) replaces the diagonal \(ac\) with \(bd\) in the quadrilateral \(abcd\). This note shows that for any closed surface \(\text{F}^ 2\), there exists a positive integer \(N\) such that two triangulations \(G\) and \(G'\) of \(\text{F}^ 2\) are equivalent to each other under diagonal flips if \(| V(G)|= | V(G')|\geq N\).
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 716459
zbMATH Keywords: triangulation
zbMATH Keywords: closed surface
zbMATH Keywords: face
zbMATH Keywords: triangular faces
zbMATH Keywords: diagonal flip
reviewed by: Alan C. Tucker
MaRDI profile type: Publication
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cites work: Q3766517
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cites work: Wie man die geschlossenen nichtorientierbaren Flächen in möglichst wenig Dreiecke zerlegen kann
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Wikidata QID: Q126582423
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description: scientific article; zbMATH DE number 716459