Vertex partition of a complete multipartite graph into two kinds of induced subgraphs

Abstract: Let , be positive integers. Let be a graph of order . It is shown that if is a complete multipartite graph, has a vertex partition such that for some pair of graphs and of order , the subgraph of induced by is isomorphic to or for any with . Furthermore, for graphs not necessarily complete multipartite, similar problems are discussed. [Copyright &y& Elsevier]