Diagonal transformations of graphs and Dehn twists of surfaces
type: Item
instance of: scholarly article
title: Diagonal transformations of graphs and Dehn twists of surfaces
zbMATH Open document ID: 0873.05040
author: Atsuhiro Nakamoto
author: Katsuhiro Ota
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-08-12T00:00:00Z
review text: The authors are interested on two simple operations in graphs, the diagonal slide and diagonal rotation. The operations replace edges shared by two adjacent quadrilateral faces on a cellular embedding of the graph in a closed surface, to produce a new embedded graph. Two graphs are equivalent if a finite sequence of these operations takes one into the other. A quadrangulation is an embedded graph whose faces are all quadrilaterals. The authors prove the following theorem: For any closed surface \(F^2\), there exists a positive integer \(M(F^2)\) such that for any pair of bipartite quadrangulations \(G_1,G_2\) with \(|V(G_1) |=|V(G_2) |\geq M(F^2)\), \(G_1\) and \(G_2\) are equivalent up to isotopy. This is a variation of other results, for the case of triangulations, due to \textit{R. Brunet}, the first author and \textit{S. Negami} [J. Comb. Theory, Ser. B 68, No. 2, 295-309, Art. No. 0070 (1996; Zbl 0861.05021)].
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1042500
zbMATH Keywords: embeddings of graphs
zbMATH Keywords: isotopy equivalence
zbMATH Keywords: Dehn twists
zbMATH Keywords: graph operations
zbMATH Keywords: topological graph theory
MaRDI profile type: Publication
OpenAlex ID: W2040118370
cites work: Q5558925
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DOI: 10.1006/JCTB.1997.1759
description: scientific article; zbMATH DE number 1042500