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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the number of Hamiltonian circuits in the $ n$-cube


Authors: E. Dixon and S. Goodman
Journal: Proc. Amer. Math. Soc. 50 (1975), 500-504
MSC: Primary 05C35
MathSciNet review: 0369157
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Abstract | References | Similar Articles | Additional Information

Abstract: Improved upper and lower bounds are found for the number of hamiltonian circuits in the $ n$-cube.


References [Enhancements On Off] (What's this?)

  • [1] Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967. MR 0226496 (37 #2085)
  • [2] E. N. Gilbert, Gray codes and paths on the 𝑛-cube, Bell System Tech. J 37 (1958), 815–826. MR 0094273 (20 #792)
  • [3] Robert J. Douglas, A note on a theorem of H. L. Abbott, Canad. Math. Bull. 13 (1970), 79–81. MR 0280397 (43 #6117)
  • [4] H. L. Abbott, Hamiltonian circuits and paths on the 𝑛-cube, Canad. Math. Bull. 9 (1966), 557–562. MR 0207580 (34 #7395)
  • [5] E. Dixon and S. Goodman, An algorithm for finding all the hamiltonian circuits and two factors in an arbitrary directed or undirected graph, DAMACS Tech. Rept., 3-73, University of Virginia, Charlottsville, Va., 1973.
  • [6] E. N. Gilbert, Private communication.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0369157-0
PII: S 0002-9939(1975)0369157-0
Keywords: Hamiltonian circuit, $ n$-cube, undirected graph, edge, node
Article copyright: © Copyright 1975 American Mathematical Society