How many conjectures can you stand: a survey

Haitze J. Broersma, Z. Ryjáček, P. Vrána

Research output: Contribution to journal › Article › Academic › peer-review

12 Citations (Scopus)
52 Downloads (Pure)

Abstract

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 languageUndefined
Pages (from-to)57-75
Number of pages19
JournalGraphs and combinatorics
Volume28
Issue number1
DOIs
Publication statusPublished - 2012

Keywords

  • Contractible graph
  • IR-79404
  • 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
  • EWI-21070
  • MSC-05C35
  • MSC-05C38
  • MSC-05C45
  • METIS-293520
  • Claw-free graph

Cite this

Broersma, Haitze J. ; Ryjáček, Z. ; Vrána, P. / How many conjectures can you stand: a survey. In: Graphs and combinatorics. 2012 ; Vol. 28, No. 1. pp. 57-75.
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Broersma, HJ, Ryjáček, Z & Vrána, P 2012, 'How many conjectures can you stand: a survey' Graphs and combinatorics, vol. 28, no. 1, pp. 57-75. https://doi.org/10.1007/s00373-011-1090-6

How many conjectures can you stand: a survey. / Broersma, Haitze J.; Ryjáček, Z.; Vrána, P.

In: Graphs and combinatorics, Vol. 28, No. 1, 2012, p. 57-75.

Research output: Contribution to journal › Article › Academic › peer-review

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AU - Vrána, P.

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KW - Collapsible graph

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KW - Dominating closed trail

KW - Dominating cycle

KW - Essentially 4-edge-connected

KW - Line graph

KW - Snark

KW - Supereulerian graph

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KW - MSC-05C45

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Broersma HJ, Ryjáček Z, Vrána P. How many conjectures can you stand: a survey. Graphs and combinatorics. 2012;28(1):57-75. https://doi.org/10.1007/s00373-011-1090-6

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