Irreducible triangulations of surfaces
type: Item
instance of: scholarly article
title: Irreducible triangulations of surfaces
zbMATH Open document ID: 0863.05029
author: Paul Seymour
author: Zhicheng Gao
author: R. B. Richter
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-02-23T00:00:00Z
review text: The authors show that, for any surface \(S\) and any \(k\), there are at most finitely many triangulations of \(S\) such that each edge is in a noncontractible cycle of length \(k\), but is in no shorter noncontractible cycle; such a triangulation is said to be \(k\)-irreducible. If \(S\) is the sphere with \(h\) handles (respectively the sphere with \(k\) crosscaps), then the Euler genus of \(S\) is \(2h\) (respectively \(k)\). Specifically, the authors show that if \(T\) is a \(k\)-irreducible triangulation of \(S\), of Euler genus \(g\), and if \(k\geq 2\), then \(|E(T)|\leq 3k\) \(k!(6k)^kg^2\).
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 954823
zbMATH Keywords: surface
zbMATH Keywords: triangulations
zbMATH Keywords: sphere
zbMATH Keywords: handles
zbMATH Keywords: crosscaps
zbMATH Keywords: Euler genus
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: jctb.1996.0064
OpenAlex ID: W1991160231
DOI: 10.1006/JCTB.1996.0064
description: scientific article; zbMATH DE number 954823