Defective Ramsey Numbers and Defective Cocolorings in Some Subclasses of Perfect Graphs

In this paper, we investigate a variant of Ramsey numbers called defective where cliques and independent sets are generalized to k-dense k-sparse sets, both commonly k-defective sets. We focus on the computation restricted some subclasses perfect graphs. Since direct proof techniques often insufficient for obtaining new values numbers, provide generic algorithm compute in given target graph class. combine with our efficient generation several graphs, bipartite graphs chordal also initiate study related parameter, denoted by \(c^{{\mathcal {G}}}_k(m)\), which is maximum order n such that vertex set any class \({\mathcal {G}}\) can be partitioned into at most m subsets each k-defective. obtain {G}}}_k(m)\) cographs.