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2008 On graphs for which every planar immersion lifts to a knotted spatial embedding
Amy DeCelles, Joel Foisy, Chad Versace, Alice Wilson
Involve 1(2): 145-158 (2008). DOI: 10.2140/involve.2008.1.145

Abstract

We call a graph G intrinsically linkable if there is a way to assign over/under information to any planar immersion of G such that the associated spatial embedding contains a pair of nonsplittably linked cycles. We define intrinsically knottable graphs analogously. We show there exist intrinsically linkable graphs that are not intrinsically linked. (Recall a graph is intrinsically linked if it contains a pair of nonsplittably linked cycles in every spatial embedding.) We also show there are intrinsically knottable graphs that are not intrinsically knotted. In addition, we demonstrate that the property of being intrinsically linkable (knottable) is not preserved by vertex expansion.

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Amy DeCelles. Joel Foisy. Chad Versace. Alice Wilson. "On graphs for which every planar immersion lifts to a knotted spatial embedding." Involve 1 (2) 145 - 158, 2008. https://doi.org/10.2140/involve.2008.1.145

Information

Received: 10 June 2007; Accepted: 1 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1154.57003
MathSciNet: MR2429655
Digital Object Identifier: 10.2140/involve.2008.1.145

Subjects:
Primary: 57M15 , 57M25

Keywords: intrinsically knotted , intrinsically linked , regular projection , spatially embedded graph

Rights: Copyright © 2008 Mathematical Sciences Publishers

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