Path factors in cubic graphs | Zendy

Kawarabayashi Kenichi | Zendy; Matsuda Haruhide | Zendy; Oda Yoshiaki | Zendy; Ota Katsuhiro | Zendy

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Path factors in cubic graphs

Author(s) -

Kawarabayashi Kenichi,

Matsuda Haruhide,

Oda Yoshiaki,

Ota Katsuhiro

Publication year - 2002

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.10022

Subject(s) - combinatorics , mathematics , cubic graph , corollary , discrete mathematics , pancyclic graph , graph factorization , distance hereditary graph , graph , symmetric graph , line graph , graph power , voltage graph , 1 planar graph

Let ℱ be a set of connected graphs. An ℱ‐factor of a graph is its spanning subgraph such that each component is isomorphic to one of the members in ℱ. Let P k denote the path of order k . Akiyama and Kano have conjectured that every 3‐connected cubic graph of order divisible by 3 has a { P 3 }‐factor. Recently, Kaneko gave a necessary and sufficient condition for a graph to have a { P 3 , P 4 , P 5 }‐factor. As a corollary, he proved that every cubic graph has a { P 3 , P 4 , P 5 }‐factor. In this paper, we prove that every 2‐connected cubic graph of order at least six has a { P k ∣ k ≥ , 6}‐factor, and hence has a { P 3 , P 4 }‐factor. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 188–193, 2002; DOI 10.1002/jgt.10022

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