Discussiones Mathematicae Graph Theory 28(3) (2008) 551-556
doi: 10.7151/dmgt.1426

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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

[1] J. Akiyama and M. Kano, Path factors of a graph, Graphs and applications (Boulder, Colo., 1982), 1-21, Wiley-Intersci. Publ., Wiley, New York, 1985.
[2] A. Kaneko, A necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two, J. Combin. Theory (B) 88 (2003) 195-218, doi: 10.1016/S0095-8956(03)00027-3.
[3] M. Kano, G.Y. Katona and Z. Király, Packing paths of length at least two, Discrete Math. 283 (2004) 129-135, doi: 10.1016/j.disc.2004.01.016.
[4] K. Kawarabayashi, H. Matsuda, Y. Oda and K. Ota, Path factors in cubic graphs, J. Graph Theory 39 (2002) 188-193, doi: 10.1002/jgt.10022.
[5] J. Petersen, Die Theorie der regulären Graphen, Acta Math. 15 (1891) 193-220, doi: 10.1007/BF02392606.

Received 28 December 2006
Revised 27 June 2008
Accepted 27 June 2008