A new polynomial cluster deletion subproblem

Cluster Deletion (CD) is a combinatorial problem which consists in transforming a given graph into a cluster graph by deleting as few edges as possible. CD arises in the field of classification when the available data is in the form of graphs. In this paper, we introduce a graph transformation which allowed the identification of new polynomially solvable classes of CD. We show that if a graph is K₃-free or (diamond, kite, house, xbanner)-free then cluster deletion can be solved in polynomial time on that graph. We also propose algorithms to detect forbidden patterns, a necessary task for identifying the discovered polynomial CD classes.