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Discrete Mathematics
Volume 302, Issues 1-3, 28 October 2005, Pages 225-242
Structural Combinatorics - Combinatorial and Computational Aspects of Optimization, Topology and Algebra
 
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doi:10.1016/j.disc.2004.07.035    
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Copyright © 2005 Elsevier B.V. All rights reserved.

Knots and links in spatial graphs: A survey

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J.L. Ramírez AlfonsínE-mail The Corresponding Author

Université Pierre et Marie Curie, Paris 6, Equipe Combinatoire - Case 189, 4 Place Jussieu Paris 75252 Cedex 05, France


Received 7 December 2001; 
revised 15 May 2003; 
accepted 22 July 2004. 
Available online 8 August 2005.

Abstract

A spatial representation, View the MathML source, of a graph G, is an embedded image of G in View the MathML source. A set of cycles in View the MathML source can be thought of as a set of simple closed curves in View the MathML source and thus they may be regarded as a link in View the MathML source. A recent area of research investigates the dependence (or independence) of the link types on the structure of the abstract graph G itself rather than on specific spatial representations of G. In this article, we survey what is known today.

Keywords: Knot; Link; Spatial graphs

Article Outline

1. Introduction
2. Concatenated graphs
3. Self-knotted graphs
4. Realizable embeddings
5. Linear embeddings
Appendix
References









Discrete Mathematics
Volume 302, Issues 1-3, 28 October 2005, Pages 225-242
Structural Combinatorics - Combinatorial and Computational Aspects of Optimization, Topology and Algebra
 
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