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A newly recognized intrinsically knotted graph
Article first published online: 20 MAY 2003
DOI: 10.1002/jgt.10114
Copyright © 2003 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. (2003), A newly recognized intrinsically knotted graph. J. Graph Theory, 43: 199–209. doi: 10.1002/jgt.10114
Publication History
- Issue published online: 20 MAY 2003
- Article first published online: 20 MAY 2003
- Manuscript Revised: 16 DEC 2002
- Manuscript Received: 11 OCT 2001
- Abstract
- References
- Cited By
Keywords:
- intrinsically knotted;
- embedded graphs;
- spatial graphs;
- minor minimal
Abstract
In [Adams, 1994; The Knot Book], Colin Adams states as an open question whether removing a vertex and all edges incident to that vertex from an intrinsically knotted graph must yield an intrinsically linked graph. In this paper, we exhibit an intrinsically knotted graph for which there is a vertex that can be removed, and the resulting graph is not intrinsically linked. We further show that this graph is minor minimal with respect to being intrinsically knotted. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 199–209, 2003