# Path and cycle factors of cubic bipartite graphs

M. Kano; Changwoo Lee; Kazuhiro Suzuki

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 3, page 551-556
- ISSN: 2083-5892

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topM. Kano, Changwoo Lee, and Kazuhiro Suzuki. "Path and cycle factors of cubic bipartite graphs." Discussiones Mathematicae Graph Theory 28.3 (2008): 551-556. <http://eudml.org/doc/270380>.

@article{M2008,

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.},

author = {M. Kano, Changwoo Lee, Kazuhiro Suzuki},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {cycle factor; path factor; bipartite graph},

language = {eng},

number = {3},

pages = {551-556},

title = {Path and cycle factors of cubic bipartite graphs},

url = {http://eudml.org/doc/270380},

volume = {28},

year = {2008},

}

TY - JOUR

AU - M. Kano

AU - Changwoo Lee

AU - Kazuhiro Suzuki

TI - Path and cycle factors of cubic bipartite graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 3

SP - 551

EP - 556

AB - 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.

LA - eng

KW - cycle factor; path factor; bipartite graph

UR - http://eudml.org/doc/270380

ER -

## References

top- [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. Zbl0587.05048
- [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. Zbl1029.05125
- [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. Zbl1042.05084
- [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. Zbl1176.05064
- [5] J. Petersen, Die Theorie der regulären Graphen, Acta Math. 15 (1891) 193-220, doi: 10.1007/BF02392606.

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