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Paul Blain, Garry Bowlin, Joel Foisy, Jacob Hendricks, and Jason LaCombe
Knotted Hamiltonian cycles in spatial embeddings of complete graphs
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| Published: |
February 20, 2007
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| Keywords: |
Spatial graph, embedded graph, intrinsically knotted |
| Subject: |
57M15, 57M25 |
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Abstract
We show the complete graph on n vertices contains a knotted
Hamiltonian cycle in every spatial embedding, for n > 7. Moreover, we show that for n >8, the minimum number of knotted Hamiltonian cycles in every embedding of Kn is at least (n-1)(n-2)...(9)(8). We also prove K8 contains at least 3 knotted Hamiltonian cycles in every spatial
embedding.
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| Acknowledgements
The results in Section 3 were obtained during an NSF and NSA-sponsored summer Research Experience for Undergraduates.
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| Author information
Paul Blain:
Department of Mathematics, University of Washington, Seattle, WA 98195-4350
pblain@math.washington.edu
Garry Bowlin:
Department of Mathematics, Binghamton University, Binghamton, NY 13902
bowlin@math.binghamton.edu
Joel Foisy:
Department of Mathematics, SUNY Potsdam, Potsdam, NY 13676
foisyjs@potsdam.edu
Jacob Hendricks:
Department of Mathematics, University of Texas at Austin, Austin, TX 78712
jhendricks@math.utexas.edu
Jason LaCombe:
Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642
jason_lacombe@urmc.rochester.edu
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