LUNE-FREE KNOT GRAPHS-Reference-Cited by-同舟云学术

LUNE-FREE KNOT GRAPHS

Published:2008-01 Issue:01 Volume:17 Page:55-74
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

ELIAHOU SHALOM¹,HARARY FRANK²,KAUFFMAN LOUIS H.³

Affiliation:

1. LMPA Joseph Liouville, FR CNRS 2956, Université du Littoral Côte d'Opale, B.P. 699, F-62229 Calais cedex, France

2. New Mexico State University Las Cruces, New Mexico, USA

3. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL, 60607-7045, USA

Abstract

This paper is an exploration of simple four-regular graphs in the plane (i.e. loop-free and with no more than one edge between any two nodes). Such graphs are fundamental to the theory of knots and links in three dimensional space, and their planar diagrams. We dedicate this paper to Frank Harary (1921–2005), whose fascination with graphs of knots inspired this work, and with whom we had the pleasure of developing this paper.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216508005963

Reference5 articles.

1. J. H. Conway, 1970 Computational Problems in Abstract Algebra (Proc. Conf. Oxford, 1967) (Pergamon, Oxford) pp. 329–358.

2. Knots and Graphs I—Arc Graphs and Colorings

3. A Census of Planar Maps

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