DEGREE CONDITIONS FOR THE EXISTENCE OF A {P2,P5}-FACTOR IN A GRAPH

A subgraph of a graph G is spanning if the subgraph covers all vertices of G. A pathfactor of a graph.. is a spanning subgraph H of G such that every component of H is a path. In this article, we prove that (i) a connected graph G with delta(G) >= 5 admits a {P-2, P-5}-factor if G satisfies delta(G) > 3 alpha(G)-1/4; (ii) a connected graph G of order n with n >= 7 has a {P-2,P-5}-factor if G satisfies max{dG (x), dG(y)} >= 3n/7 for any two nonadjacent vertices x and y of G.