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Hamiltonian Circuits on the N-Cube

Published online by Cambridge University Press:  20 November 2018

D. H. Smith
D. H. Smith*
Affiliation:
Glamorgan Polytechnic, Treforest, Wales, U.K.
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The problem of finding bounds for the number h(n) of Hamiltonian circuits on the n-cube has been studied by several authors, (1), (2), (3). The best upper bound known is due to Larman (5) who proved that .

In this paper we use a result of Nijenhuis and Wilf (4) on permanents of (0, 1)- matrices to show that for n≥5

where τ, a and c are constants.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 759 - 761
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Abbott, H. L., Hamiltonian circuits and paths on the n-cube, Canad. Math. Bull. 9(5) 1966, 557–562.Google Scholar
2. Douglas, R. J., A note on a theorem of H. L. Abbott, Canad. Math. Bull. 13(1) 1970, 79–81.Google Scholar
3. Gilbert, E. N., Gray codes and paths on the n-cube, Bell. Syst. Tech. J. 37 (1958), 815–826.Google Scholar
4. Nijenhuis, A. and Wilf, H. S., On a conjecture in the theory of permanents, Bull. A. M. S. 76 (1970) 738–739.Google Scholar
5. Larman, D. G., Private communication.Google Scholar