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2-Factors in Claw-Free Graphs with Lower Bounds Cycle Lengths

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Abstract

For a graph G, we denote by δ(G) the minimum degree of G. A graph G is said to be claw-free if G has no induced subgraph isomorphic to K 1, 3. In this article, we prove that every claw-free graph G with minimum degree at least 4 has a 2-factor in which each cycle contains at least \({\big\lceil\frac{\delta(G) - 1}{2}\big\rceil}\) vertices and every 2-connected claw-free graph G with minimum degree at least 3 has a 2-factor in which each cycle contains at least δ(G) vertices. For the case where G is 2-connected, the lower bound on the length of a cycle is best possible.

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Authors and Affiliations

  1. Department of Mathematics, NTIS, New Technologies for the Information Society, University of West Bohemia, Univerzitní 8, 306 14, Plzeň, Czech Republic

    Roman Čada

  2. CE-ITI, European Center of Excellence, University of West Bohemia, Univerzitní 8, 306 14, Plzeň, Czech Republic

    Roman Čada

  3. Department of Mathematics and Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto, 860-8555, Japan

    Shuya Chiba

  4. Department of Mathematics, College of Science and Technology, Nihon University, Tokyo, 101-8308, Japan

    Kiyoshi Yoshimoto

Authors
  1. Roman Čada
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  2. Shuya Chiba
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  3. Kiyoshi Yoshimoto
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Corresponding author

Correspondence to Shuya Chiba.

Additional information

An extended abstract has been published in EuroComb2011, Electronic Notes in Discrete Mathematics Vol. 38 (2011) 213–219.

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Čada, R., Chiba, S. & Yoshimoto, K. 2-Factors in Claw-Free Graphs with Lower Bounds Cycle Lengths. Graphs and Combinatorics 31, 99–113 (2015). https://doi.org/10.1007/s00373-013-1375-z

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  • DOI: https://doi.org/10.1007/s00373-013-1375-z

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