A new polynomial class of cluster deletion problem

Cluster Deletion (CD) problem asks to transform a given graph into a cluster graph by at most k edge deletions. CD is a combinatorial problem arising in the field of classification. In this paper, we introduce a graph transformation which enabled the identification of new polynomially solvable classes of CD problem. We show that if a graph is K
₃
-free or (diamond, kite, house, xbanner)-free then cluster deletion problem can be solved in polynomial time on that graph.