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This paper reviews a dynamic programming procedure for the partitioning of connected graphs with integer-weighted nodes and positive valued edges. The upper bound on the number of feasible partitions generated using this technique is shown to grow factorially in the number of graph nodes. The use of graph properties is then introduced to reduce the number of feasible partitions generated in the determination of the optimal partition. Depending upon the structure of the graph, the use of these properties can cause a significant reduction in the computation time and storage space required to partition the graph.
Jaroslav Lukeš (Sat,) studied this question.