On the nonembeddability and crossing numbers of some Kleinical polyhedral maps on the torus
type: Item
instance of: scholarly article
title: On the nonembeddability and crossing numbers of some Kleinical polyhedral maps on the torus
zbMATH Open document ID: 1062.05049
author: Adrian Riskin
published in: Graphs and Combinatorics
publication date: 2005-05-12T00:00:00Z
review text: The graphical Cartesian product \(C_n \times C_m\) embeds nicely on the torus and is known as the toroidal grid. The author defines similar grids on the Klein bottle. He then gives a property of Kleinical graphs that ensures the graphs are not toroidal; namely, that the graphs have four disjoint cycles such that deleting each from the embedding in the Klein bottle gives a cylinder. Using this property, he finds the crossing number on the torus of two infinite classes of the Kleinical grids.
reviewed by: Dan S. Archdeacon
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 2168058
zbMATH Keywords: Crossing numbers
zbMATH Keywords: Reimbedding
zbMATH Keywords: Nontoroidal graphs
MaRDI profile type: Publication
full work available at URL: s00373-004-0589-5
OpenAlex ID: W2058156560
DOI: 10.1007/S00373-004-0589-5
description: scientific article; zbMATH DE number 2168058