New York Journal of Mathematics
Volume 13 (2007) 11-16

Volume 13

NYJM Home

Editorial Board

NYJM Monographs

Full Text Index

For Authors
  

Paul Blain, Garry Bowlin, Joel Foisy, Jacob Hendricks, and Jason LaCombe

Knotted Hamiltonian cycles in spatial embeddings of complete graphs

Published: February 20, 2007
Keywords: Spatial graph, embedded graph, intrinsically knotted
Subject: 57M15, 57M25
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.
Acknowledgements

The results in Section 3 were obtained during an NSF and NSA-sponsored summer Research Experience for Undergraduates.
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