Randomly P₃-extendable Graphs

Let G be a graph and K be a given connected graph. A subgraph H of G is called aK-packing if every component of H is isomorphic to K. In particular, if V (H) = V (G), His called a K-factor of G. We say G is randomly K-extendable if for any K-packing H of G,there exists a K-factor H of G containing H. In this paper we characterize the structureand property of randomly P₃-extendable graphs. It is shown that a connected graph Gof order n = 3k for some positive integer k≥3 is randomly P₃-extendable if and only ifδ(G)≥n - 2.