Path and cycle factors of cubic bipartite graphs
Mikio Kanō, Changwoo Lee, Kazuhiro Suzuki · Discussiones Mathematicae Graph Theory · 2008
For a set S of connected graphs, a spanning subgraph F of a graph is called an S-factor if every component of F is isomorphic to a member of S. It was recently shown that every 2-connected cubic graph has a {Cn|n ≥ 4}-factor and a {Pn|n ≥ 6}-factor, where Cn and Pn 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 {Cn|n ≥ 6}-factor, and has a {Pn|n ≥ 8}-factor if its order is at least 8.