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

Abstract

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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.

How to cite

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M. 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

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  1. [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. [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. [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. [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. [5] J. Petersen, Die Theorie der regulären Graphen, Acta Math. 15 (1891) 193-220, doi: 10.1007/BF02392606. 

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