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The number of Hamiltonian circuits in large, heavily edged graphs

Published online by Cambridge University Press:  18 May 2009

J. Sheehan  and
E. M. Wright
J. Sheehan
Affiliation:
University of Aberdeen, Aberdeen, U.K.
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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 write

and 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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 35 - 37
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

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4.Wright, E. M., For how many edges is a graph almost certainly Hamiltonian?, J. London Math. Soc. (2) 8 (1974), 44–48.CrossRefGoogle Scholar