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The group of classical graph-theoretic problems, including graph colouring, clique cover, and maximal clique, may be viewed as instances of a general node partitioning problem (NPP). A wide variety of real life problems can be modelled as instances of NPP. Finding an optimal partition for the NPP is said to be NP-complete. A stochastic search by a genetic algorithm (GA) is employed to find a near optimal solution for the NPP. The critical aspects of the GA for NPP, such as the solution representation by elegant data structure, together with genetic operations and selection policies employed in the GA procedure, are also presented. The proposed GA does not require the number of disjunct node sets to be given a priori. Three application problems in VLSI design are solved as instances of NPP. The experimental results presented in each case of these application problems bring out the efficacy of genetic algorithms.