摘要
Ler G = ( V, E) be a finite simple graph and Pn 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.
Ler G = ( V, E) be a finite simple graph and Pn 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.