Nonrevisiting cycles on surfaces
type: Item
instance of: scholarly article
title: Nonrevisiting cycles on surfaces
zbMATH Open document ID: 0938.05026
DOI: 10.1016/S0012-365X(99)00046-1
published in: Discrete Mathematics
publication date: 2000-01-03T00:00:00Z
review text: A nonrevisiting cycle is a nonplanar cycle, in a polyhedral map \(M\), whose intersection with each face of \(M\) is either connected or empty. \textit{D. W. Barnette} [Discrete Math. 70, No. 1, 1-16 (1988; Zbl 0654.05024)] showed that the torus \(S_1\), the projective plane \(N_1\), and the Klein bottle \(N_2\) have such cycles. The present author uses a polygonal representation of a polyhedral map to extend Barnette's results to a class of polyhedral maps on \(S_2\) and \(N_3\).
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1382642
zbMATH Keywords: nonrevisiting cycle
zbMATH Keywords: polyhedral map
zbMATH Keywords: torus
zbMATH Keywords: projective plane
zbMATH Keywords: Klein bottle
author: Hari Pulapaka
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00046-1
OpenAlex ID: W2001646509
description: scientific article; zbMATH DE number 1382642