Generating triangulations on closed surfaces with minimum degree at least 4
type: Item
instance of: scholarly article
title: Generating triangulations on closed surfaces with minimum degree at least 4
zbMATH Open document ID: 0995.05043
DOI: 10.1016/S0012-365X(01)00093-0
author: Atsuhiro Nakamoto
author: Seiya Negami
published in: Discrete Mathematics
publication date: 2002-05-21T00:00:00Z
review text: The authors show that every triangulation of a closed surface \(S\), other than the sphere, having minimum degree at least 4 can be obtained from an irreducible triangulation of \(S\) by two types of local deformation: (1) ``splitting'' a vertex into two adjacent vertices of degree at least 4 (reversing an edge contraction) and (2) ``adding an octahedron'' by completing the graph \(K_{2,2,2}\) within a given triangle. They also show that every triangulation of the sphere having minimum degree at least 4 can be obtained from \(K_{2,2,2}\) by using (1) and (2).
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1743034
zbMATH Keywords: triangulation
zbMATH Keywords: closed surface
zbMATH Keywords: sphere
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00093-0
OpenAlex ID: W2025373406
description: scientific article; zbMATH DE number 1743034