Maximum covering with D-cliques

Given a graph G = (V, E), we consider the problem to find a set of D pairwise disjoint cliques in it with maximum overall number of vertices. We determine the computational complexity of this problem restricted to a variety of different graph classes. We give polynomial time algorithms for the problem restricted to interval graphs, bipartite graphs, cographs, directed path graphs and partial k-trees. In contrast, we show the NP-completeness for undirected path graphs.\u3cbr/\u3e\u3cbr/\u3