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The number of sparsely edged labelled Hamiltonian graphs

Published online by Cambridge University Press:  18 May 2009

E. M. Wright
E. M. Wright
Affiliation:
University of Aberdeen, Scotland
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An (n, q) graph is a graph on n labelled points and q lines, no loops and no multiple lines. We write N = ½n(n – 1), B(a, b) = a!/{b!(a – b)!} and B(a, 0) = 1, so that there are just B(N, q)different (n, q) graphs. Again h(n, q) is the number of Hamiltonian (n, q) graphs. Much attention has been devoted to the problem of determining for which q = q(n) “almost all” (n, q) graphs are Hamiltonian, i.e. for which q we have

as n → ∞. I proved [8, Theorem 4] that qn–3/2; → ∞ is a sufficient condition by showing that, for such q, almost all (n, q) graphs have about the average number of Hamiltonian circuits (H.c.s).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983 , pp. 83 - 87
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

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