Optimal clustering of multipartite graphs Original Research Article

Given a graph image, the problem dealt within this paper consists in partitioning X into a disjoint union of cliques by adding or removing a minimum number image of edges (Zahnʹs problem). While the computation of image is NP-hard in general, we show that its computation can be done in polynomial time when G is bipartite, by relating it to a maximum matching problem. When G is a complete multipartite graph, we give an explicit formula specifying image with respect to some structural features of G. In both cases, we give also the structure of all the optimal clusterings of G.