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2012 Partial duals of plane graphs, separability and the graphs of knots
Iain Moffatt
Algebr. Geom. Topol. 12(2): 1099-1136 (2012). DOI: 10.2140/agt.2012.12.1099

Abstract

There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedded graph represents a link diagram. Furthermore, although a Tait graph describes a unique link diagram, the same embedded graph can represent many different link diagrams. One is then led to ask which embedded graphs represent link diagrams, and how link diagrams presented by the same embedded graphs are related to one another. Here we answer these questions by characterizing the class of embedded graphs that represent link diagrams, and then using this characterization to find a move that relates all of the link diagrams that are presented by the same set of embedded graphs.

Citation

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Iain Moffatt. "Partial duals of plane graphs, separability and the graphs of knots." Algebr. Geom. Topol. 12 (2) 1099 - 1136, 2012. https://doi.org/10.2140/agt.2012.12.1099

Information

Received: 10 January 2012; Revised: 23 February 2012; Accepted: 25 February 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1245.05030
MathSciNet: MR2928906
Digital Object Identifier: 10.2140/agt.2012.12.1099

Subjects:
Primary: 05C10, 57M15
Secondary: 05C75, 57M25

Rights: Copyright © 2012 Mathematical Sciences Publishers

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