Closure concepts for claw-free graphs

Haitze J. Broersma, H. Trommel

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Recently, Ryjácek introduced an interesting new closure concept for claw-free graphs, and used it to prove that every nonhamiltonian claw-free graph is a spanning subgraph of a nonhamiltonian line graph (of a triangle-free graph). We discuss the relationship between Ryjácek's closure and the K4-closure introduced by the first author. Our main result deals with a variation on the K4-closure. It implies a simpler proof of Ryjá ek's closure theorem, and yields a more general closure concept which is not restricted to claw-free graphs only.
Original languageEnglish
Pages (from-to)231-238
Number of pages8
JournalDiscrete mathematics
Issue number185
Publication statusPublished - 1998


  • (Hamilton) cycle
  • (Long
  • Circumference
  • METIS-140550
  • Closure
  • IR-73869
  • Claw-free graph

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