Geodesic
The number of Hamiltonian circuits in large, heavily edged graphs
Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 35-37

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G is a graph on n nodes with q edges, without loops or multiple edges. We write α = q/n and β for the maximum degree of any node of G. We writeand H for the number of Hamiltonian circuits (H.c.) in the complement of G, or, what is the same thing, the number of those H.c. in the complete graph Kn which have no edge in common with G. Our object here is to prove the following theorem. 
Sheehan, J. The number of Hamiltonian circuits in large, heavily edged graphs. Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 35-37. doi: 10.1017/S0017089500003001
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