Path and cycle factors of cubic bipartite graphs

Abstract

For a set S of connected graphs, a spanning subgraph F of a graph is called an Sfactor if every component of F is isomorphic to a member of S. It was recently shown that every 2-connected cubic graph has a {C n |n ≥ 4}-factor and a {P n |n ≥ 6}factor, where C n and P n denote the cycle and the path of order n, respectively (Kawarabayashi et al., J. Graph Theory, Vol.39 (2002) 188-193).In this paper, we show that every connected cubic bipartite graph has a {C n |n ≥ 6}-factor, and has a {P n |n ≥ 8}-factor if its order is at least 8.