How many conjectures can you stand? A survey

H.J. Broersma*, Z. Ryjáček, P. Vrána

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)
111 Downloads (Pure)


We survey results and open problems in hamiltonian graph theory centered around two conjectures of the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian. These conjectures have lead to a wealth of interesting concepts, techniques, results and equivalent conjectures.
Original languageEnglish
Pages (from-to)57-75
Number of pages19
JournalGraphs and combinatorics
Issue number1
Publication statusPublished - 2012


  • Contractible graph
  • Closure
  • Cyclically 4-edge-connected
  • Cubic graph
  • Collapsible graph
  • Hamilton-connected
  • Hamiltonian graph
  • Dominating closed trail
  • Dominating cycle
  • Essentially 4-edge-connected
  • Line graph
  • Snark
  • Supereulerian graph
  • MSC-05C35
  • MSC-05C38
  • MSC-05C45
  • Claw-free graph


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