Diagonal flips in outer-Klein-bottle triangulations
type: Item
instance of: scholarly article
title: Diagonal flips in outer-Klein-bottle triangulations
zbMATH Open document ID: 0964.05021
DOI: 10.1016/S0012-365X(00)00004-2
author: N. Delaunay
published in: Discrete Mathematics
publication date: 2001-01-30T00:00:00Z
review text: The present paper deals with outer-Klein-bottle triangulations, i.e. two-cell embeddings of simple graphs \(G\) into the Klein bottle such that (i) each face is bounded by a cycle; (ii) there is a specific face \(F\), called outer face, on whose boundary cycle all vertices of \(G\) appear; and (iii) other faces are all triangular. In particular, the complete list of the 33 irreducible outer-Klein-bottle triangulations is determined (starting from the complete list of the 25 irreducible triangulations of the Klein bottle, obtained by \textit{S. Lawrencenko} and \textit{S. Negami} [J. Comb. Theory, Ser. B 70, No. 2, 265-291 (1997; Zbl 0876.05023)]). Moreover, any two outer-Klein-bottle triangulations with the same number of vertices are proved to be transformed into each other by a sequence of diagonal flips (see, for example, \textit{S. Negami} [Discrete Math. 135, No. 1-3, 225-232 (1994; Zbl 0823.05028)]).
reviewed by: Maria Rita Casali
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 1506816
zbMATH Keywords: outer-Klein-bottle triangulations
zbMATH Keywords: two-cell embeddings
zbMATH Keywords: irreducible triangulations
zbMATH Keywords: diagonal flips
MaRDI profile type: Publication
full work available at URL: s0012-365x(00)00004-2
OpenAlex ID: W2099135844
description: scientific article; zbMATH DE number 1506816