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This paper considers problems of the following type: given an edgeweighted k-colored input graph with maximum color class size c, find a minimum or maximum c-way cut such that each color class is totally partitioned. Equivalently, given a weighted complete k-partite graph, cover its vertices with a minimum number of disjoint cliques in such a way that the total weight of the cliques is maximized or minimized. Our study was motivated by some work called the index domain alignment problem  ,doi:10.7155/jgaa.00021 fatcat:3rrl52falnfwnhv3rdvfivl4tu