Toroidal embeddings of abstractly planar graphs are knotted or linked
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Published Version
Author(s)
Barthel
Buck, D
Type
Journal Article
Abstract
We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus T2⊂R3 and that contain neither a nontrivial knot nor a nonsplit link into the plane. It follows that ravels do not embed on the torus. Our results provide general insight into properties of molecules that are synthesized on a torus.
Date Issued
2013-05-31
Date Acceptance
2015-05-18
Citation
Journal of Mathematical Chemistry, 2013, 53 (8), pp.1772-1790
ISSN
1572-8897
Publisher
Springer Verlag (Germany)
Start Page
1772
End Page
1790
Journal / Book Title
Journal of Mathematical Chemistry
Volume
53
Issue
8
Copyright Statement
© The Author(s) 2015. This article is published with open access at Springerlink.com. This article is distributed under the terms of the Creative Commons Attribution 4.0 International
License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.
License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.
License URL
Subjects
Topological graphs
Templating on a toroidal substrate
Knots and links
05C10
92E10
57M25
Publication Status
Published