Degree conditions for the existence of a {P2, P5}-factor in a graph

Abstract

A subgraph of a graph G is spanning if the subgraph covers all vertices of G. A path- factor of a graph G 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 δ(G) ≥ 5 admits a {P2, P5}-factor if G satisfies δ(G) > 3α(G)-1/4; (ii) a connected graph G of order n with n ≥ 7 has a {P2, P5}-factor if G satisfies max{dG(x), dG(y)} ≥ 3n/7 for any two nonadjacent vertices x and y of G.