## PATH AND CYCLE FACTORS OF CUBIC BIPARTITE GRAPHS

M. Kano1, Changwoo Lee2 and Kazuhiro Suzuki1

1Department of Computer and Information Sciences
Ibaraki University, Hitachi 316-8511, Japan
and
2Department of Mathematics, University of Seoul
Dongdaemoonku, Seoul 130-743, Korea

e-mail: kano@mx.ibaraki.ac.jp
e-mail: tutetuti@dream.com

Dedicated to Professor Hikoe Enomoto on his 60th Birthday

## Abstract

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.

Keywords: cycle factor, path factor, bipartite graph.

2000 Mathematics Subject Classification: 05C38, 05C70.

## References

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