On the ｛P₂,P₃｝-Factor of Cubic Graphs

Let G=（V,E） be a finite simple graph and P_n denote the path of order n. A spanning subgraph F is called a ｛P₂,P₃｝-factor of G if each component of F is isomorphic to P₂ or P₃. With the path-covering method, it is proved that any connected cubic graph with at least 5 vertices has a ｛P₂,P₃｝-factor F such that |P₃（F）|≥|P₂（F）|, where P₂（F） and P₃（F） denote the set of components of P₂ and P₃ in F, respectively.