On graphs for which every planar immersion lifts to a knotted spatial embedding
type: Item
instance of: scholarly article
title: On graphs for which every planar immersion lifts to a knotted spatial embedding
zbMATH Open document ID: 1154.57003
author: Joel Foisy
author: Chad Versace
author: Alice Wilson
author: Amy T. DeCelles
published in: Involve
publication date: 2008-09-04T00:00:00Z
review text: A graph is intrinsically linked (respectively knotted) if, for every planar immersion of the graph, \textit{every} assignment of a crossing structure results in a diagram for a spatial graph that contains a pair of linked cycles (respectively a knotted cycle). A graph is intrinsically linkable (respectively knottable) if, for every planar immersion of the graph, there exists \textit{an} assignment of a crossing structure that results in a diagram for a spatial graph that contains a pair of linked cycles (respectively a knotted cycle). This paper is largely concerned with the distinction between intrinsically linkable (respectively knottable) and intrinsically linked (respectively knotted) graphs. In this paper the authors provide examples of intrinsically linkable graphs that are not intrinsically linked and examples of intrinsically knottable graphs that are not intrinsically knotted. These examples show that although an intrinsically linked (respectively knotted) graph is necessarily intrinsically linkable (respectively knottable), the converse is not true. Examples are also given to show that the property of a graph being intrinsically linkable (respectively knottable) is not preserved by vertex expansion.
reviewed by: Iain Moffatt
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5320748
zbMATH Keywords: spatial graphs
zbMATH Keywords: intrinsically linkable
zbMATH Keywords: intrinsically knottable
zbMATH Keywords: intrinsically linked
zbMATH Keywords: intrinsically knotted
zbMATH Keywords: vertex expansion
MaRDI profile type: Publication
full work available at URL: involve.2008.1.145
OpenAlex ID: W2166705891
DOI: 10.2140/INVOLVE.2008.1.145
description: scientific article; zbMATH DE number 5320748