Graphs and Combinatorics

, 25:427 | Cite as

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

  • Hajo Broersma
  • Daniël Paulusma
  • Kiyoshi Yoshimoto


Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n − 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most (n − 3)/(δ − 1) components, unless G is a complete graph. These bounds are best possible in the sense that we cannot replace 5/18 by a smaller quotient and we cannot replace δ − 1 by δ, respectively.


Claw-free graph 2-factor minimum degree edge-degree 


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Copyright information

© Springer 2009

Authors and Affiliations

  • Hajo Broersma
    • 1
  • Daniël Paulusma
    • 1
  • Kiyoshi Yoshimoto
    • 2
  1. 1.Department of Computer ScienceDurham University, Science LaboratoriesDurhamEngland
  2. 2.Department of MathematicsCollege of Science and Technology, Nihon UniversityTokyoJapan

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