Geodesic
Hamiltonian Circuits on the N-Cube
Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 759-761

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Smith, D. H. Hamiltonian Circuits on the N-Cube. Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 759-761. doi: 10.4153/CMB-1974-137-9
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[1] 1. Abbott, H. L., Hamiltonian circuits and paths on the n-cube, Canad. Math. Bull. 9(5) 1966, 557–562. Google Scholar

[2] 2. Douglas, R. J., A note on a theorem of H. L. Abbott, Canad. Math. Bull. 13(1) 1970, 79–81. Google Scholar

[3] 3. Gilbert, E. N., Gray codes and paths on the n-cube, Bell. Syst. Tech. J. 37 (1958), 815–826. Google Scholar

[4] 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] 5. Larman, D. G., Private communication. Google Scholar

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