Abstract:For a set of connected graphs, a spanning subgraph of a graph is called an -factor if every component of is isomorphic to a member of . It was recently shown by Kawarabayashi et al. that every 2-connected cubic graph has a -factor and -factor, where denote the cycle of order n and denote the path of order n. Kano et al. show that every connected cubic bipartite graph has a -factor and -factor if its order is at least 8. And they have conjectured that every 3-connected cubic graph of order at least six has a -factor. In this paper, we give a proof of this conjecture.