Path factors in cubic graphs

  • Authors:

  • Ken-ichi Kawarabayashi;Haruhide Matsuda;Yoshiaki Oda;Katsuhiro Ota

  • Affiliations:

  • Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 Japan;Department of General Education, Kyushu Tokai University, Choyo, Aso, Kumamoto 869-1404 Japan;Department of Mathematics and Computer Science, Shimane University, 1060 Nishikawatsu-cho, Matsue 690-8504 Japan;Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 Japan

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2002

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Abstract

Let ℱ be a set of connected graphs. An ℱ-factor of agraph is its spanning subgraph such that each component isisomorphic to one of the members in ℱ. LetPk denote the path of order k. Akiyama andKano have conjectured that every 3-connected cubic graph of orderdivisible by 3 has a {P3}-factor. Recently,Kaneko gave a necessary and sufficient condition for a graph tohave a {P3, P4,P5}-factor. As a corollary, he proved that everycubic graph has a {P3, P4,P5}-factor. In this paper, we prove that every2-connected cubic graph of order at least six has a{Pk | k ≥ , 6}-factor, and hence has a{P3, P4}-factor. © 2002Wiley Periodicals, Inc. J Graph Theory 39: 188193, 2002; DOI10.1002-jgt.10022