Nesting points in the sphere
type: Item
instance of: scholarly article
title: Nesting points in the sphere
zbMATH Open document ID: 0995.05041
DOI: 10.1016/S0012-365X(01)00072-3
published in: Discrete Mathematics
publication date: 2002-05-21T00:00:00Z
review text: Let \(G\) be a graph imbedded in the sphere \(S\), with \(x\) a point of \(S-G\). A \(k\)-nest of \(x\) is a collection of cycles \(C_1,\dots, C_k\) of \(G\) so that for each \(i\), the side of \(C_i\) containing \(x\) also contains \(C_j\) for all \(j< i\). Then \(G\) is \(k\)-nested if every point \(x\) in \(S-G\) has a \(k\)-nest. The authors find the minor-minimal \(k\)-nested spherical maps for small \(k\). In particular, they find the obstructions (under the minor order) for the class of planar maps having a face whose boundary meets all other face boundaries.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1743007
zbMATH Keywords: sphere
zbMATH Keywords: spherical maps
zbMATH Keywords: minor
zbMATH Keywords: planar maps
zbMATH Keywords: boundary
author: Dan S. Archdeacon
author: Feliú Sagols
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00072-3
OpenAlex ID: W2133589849
description: scientific article; zbMATH DE number 1743007