Graphs and Combinatorics

, Volume 32, Issue 6, pp 2393–2413 | Cite as

On the Choosability of Claw-Free Perfect Graphs

  • Sylvain Gravier
  • Frédéric Maffray
  • Lucas Pastor
Original Paper


It has been conjectured that for every claw-free graph G the choice number of G is equal to its chromatic number. We focus on the special case of this conjecture where G is perfect. Claw-free perfect graphs can be decomposed via clique-cutset into two special classes called elementary graphs and peculiar graphs. Based on this decomposition we prove that the conjecture holds true for every claw-free perfect graph with maximum clique size at most 4.


List-coloring Choosability Claw-free Perfect 


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Copyright information

© Springer Japan 2016

Authors and Affiliations

  • Sylvain Gravier
    • 1
  • Frédéric Maffray
    • 2
  • Lucas Pastor
    • 3
  1. 1.CNRS, Institut FourierUniversity of GrenobleGrenobleFrance
  2. 2.CNRS, Laboratoire G-SCOPUniversity of GrenobleGrenobleFrance
  3. 3.Laboratoire G-SCOPUniversity of GrenobleGrenobleFrance

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