Efficient Generation of Graphical Partitions

Abstract Given a positive even integer n, we show how to generate the set G(n) of graphical partitions of n, that is, those partitions of n which correspond to the degree sequences of simple, undirected graphs. The algorithm is based on a recurrence for G(n), and the total time used by the algorithm, independent of output, is O (¦G(n)¦) , which is constant average time per graphical partition. This is the first algorithm shown to achieve such efficiency for generating G(n) and the direct approach differs from earlier ‘generate and reject’ schemes and the ‘interval/gap’ approach.