Enumeration of Large Combinatorial Structures.
Final technical rept. Nov 74-Nov 75,
ABERDEEN UNIV (SCOTLAND)
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The author developed a recurrence method to obtain an exact formula for successive k for the number of graphs with n labelled nodes and nk edges. Asymptotic results follow for large n. He also gives an account, including several new results, of the asymptotic enumeration theory for unlabelled n,q graphs which he developed over the last few years. A detailed proof is given of results about the probability of a graph being Hamiltonian and a short account of bounds on the degrees of nodes in almost all graphs. Finally, a paper is appended on refining partitions into unequal parts which adds to results due to Erdos, Guy and Moon.
- Numerical Mathematics