The crossing number of \(P(N,3)\)
type: Item
instance of: scholarly article
title: The crossing number of \(P(N,3)\)
zbMATH Open document ID: 0999.05022
author: R. B. Richter
author: Gelasio Salazar
published in: Graphs and Combinatorics
publication date: 2002-07-29T00:00:00Z
review text: The authors show that the crossing number of the generalized Petersen graph \(P(3k+ h,3)\) is \(k+h\) if \(h= 0\) or \(2\), \(k+3\) if \(h=1\), for each \(k> 2\), except that \(P(9,3)\) has crossing number \(2\). They comment as follows: A few years ago \textit{S. Fiorini} [Ann. Discrete Math. 30, 225-241 (1986; Zbl 0595.05030)] claimed to have determined the crossing numbers of certain families of generalized Petersen graphs. Unfortunately, his paper contains one serious mistake that invalidates the principal results. Our aim in this article is to present correct proofs of the main statements in Fiorini's paper, and to extend these results by determining the crossing numbers of a family of graphs for which Fiorini had only claimed upper and lower bounds.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1773386
zbMATH Keywords: crossing number
zbMATH Keywords: Petersen graph
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: s003730200028
OpenAlex ID: W2069852972
DOI: 10.1007/S003730200028
description: scientific article; zbMATH DE number 1773386