### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 57-75 |

Number of pages | 19 |

Journal | Graphs and combinatorics |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - 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

*Graphs and combinatorics*,

*28*(1), 57-75. https://doi.org/10.1007/s00373-011-1090-6

}

*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.

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

TY - JOUR

T1 - How many conjectures can you stand: a survey

AU - Broersma, Haitze J.

AU - Ryjáček, Z.

AU - Vrána, P.

N1 - Open Access

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Contractible graph

KW - IR-79404

KW - Closure

KW - Cyclically 4-edge-connected

KW - Cubic graph

KW - Collapsible graph

KW - Hamilton-connected

KW - Hamiltonian graph

KW - Dominating closed trail

KW - Dominating cycle

KW - Essentially 4-edge-connected

KW - Line graph

KW - Snark

KW - Supereulerian graph

KW - EWI-21070

KW - MSC-05C35

KW - MSC-05C38

KW - MSC-05C45

KW - METIS-293520

KW - Claw-free graph

U2 - 10.1007/s00373-011-1090-6

DO - 10.1007/s00373-011-1090-6

M3 - Article

VL - 28

SP - 57

EP - 75

JO - Graphs and combinatorics

JF - Graphs and combinatorics

SN - 0911-0119

IS - 1

ER -