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Intrinsically knotted graphs
Article first published online: 23 JAN 2002
DOI: 10.1002/jgt.10017
Copyright © 2002 Wiley Periodicals, Inc.
1097-0118/asset/cover.gif?v=1&s=747ee645df081de59c78864878c8bdb9daeca9a1 "Journal of Graph Theory")
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How to Cite
Foisy, J. (2002), Intrinsically knotted graphs. J. Graph Theory, 39: 178–187. doi: 10.1002/jgt.10017
Publication History
- Issue published online: 23 JAN 2002
- Article first published online: 23 JAN 2002
- Manuscript Revised: 26 JUL 2001
- Manuscript Received: 23 JUN 2000
- Abstract
- References
- Cited By
Keywords:
- intrinsically knotted;
- self-knotted;
- embedded graphs;
- spatial graphs;
- minor minimal
Abstract
In 1983, Conway and Gordon [J Graph Theory 7 (1983), 445–453] showed that every (tame) spatial embedding of K7, the complete graph on 7 vertices, contains a knotted cycle. In this paper, we adapt the methods of Conway and Gordon to show that K3,3,1,1 contains a knotted cycle in every spatial embedding. In the process, we establish that if a graph satisfies a certain linking condition for every spatial embedding, then the graph must have a knotted cycle in every spatial embedding. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 178–187, 2002; DOI 10.1002/jgt.10017