Nonrevisiting paths on surfaces
type: Item
instance of: scholarly article
title: Nonrevisiting paths on surfaces
zbMATH Open document ID: 0856.52012
DOI: 10.1007/BF02711500
author: Andrew Vince
author: Hari Pulapaka
published in: Discrete \& Computational Geometry
publication date: 1997-02-17T00:00:00Z
review text: The non-revisiting path conjecture for a polyhedral map would claim that between any two of its vertices there exists an edge-path which, once it leaves a face, never revisits it. This conjecture is known to be true for such maps on the sphere, projective plane, torus and Klein bottle. \textit{D. W. Barnette} [Geom. Dedicata 46, No. 2, 211-214 (1993; Zbl 0777.52007)] gave counter-examples on the orientable surface of genus 8, and the non-orientable surface of genus 16. In this paper, the authors provide counter-examples for all surfaces except for the first four, and the connected sum of three copies of the projective plane, for which the problem remains open.
Mathematics Subject Classification ID: 52B70
zbMATH DE Number: 881220
zbMATH Keywords: Hirsch conjecture
zbMATH Keywords: non-revisiting path conjecture
zbMATH Keywords: polyhedral map
zbMATH Keywords: genus
reviewed by: Peter McMullen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 881220