Connected factors in -free graphs containing an -factor

Abstract: A graph G is called -free if G has no induced subgraph isomorphic to . Let n, a, b be integers with , , and . We prove that every connected -free graph G has a connected -factor if G contains an -factor. This result is sharp in the sense that there exists a connected -free graph which has an -factor but no connected -factor for . [Copyright &y& Elsevier]