Claw-free graphs. IV. Decomposition theorem

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A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful way.

Original languageEnglish (US)
Pages (from-to)839-938
Number of pages100
JournalJournal of Combinatorial Theory. Series B
Issue number5
StatePublished - Sep 2008

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


  • Claw-free graphs
  • Induced subgraphs


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