Sufficient conditions for graphs with {P2, P5}-factors

Abstract

For a graph G, a spanning subgraph F of G is called an {P2, P5}-factor if every component of F is isomorphic to P2 or P5, where Pk denotes the path of order k. It was proved by Egawa and Furuya that if G satisfies 3c1 (G − S) + 2c3 (G − S) ≤ 4|S| + 1 for all S ⊆ V(G), then G has a {P2, P5}-factor, where ck (G − S) denotes the number of components of G − S with order k. By this result, we give some other sufficient conditions for a graph to have a {P2, P5}-factor by various graphic parameters such as toughness, binding number, degree sums, etc. Moreover, we obtain some regular graphs and some K(1,r)-free graphs having {P2, P5}-factors.