A *platypus graph* is a non-hamiltonian graph for which every vertex-deleted subgraph is traceable (i.e. contains a hamiltonian path).

The graph lists are currently only available in 'graph6' format.

All results were obtained with the program GenHypohamiltonian, see [1] for details.

The following table gives the complete lists of all platypus graphs with a given lower bound on the girth.

Vertices | girth ≥ 3 | girth ≥ 4 | girth ≥ 5 | girth ≥ 6 | girth ≥ 7 | girth ≥ 8 | girth ≥ 9 |
---|---|---|---|---|---|---|---|

0-8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |

10 | 48 | 2 | 2 | 0 | 0 | 0 | 0 |

11 | 814 | 4 | 3 | 0 | 0 | 0 | 0 |

12 | 24847 | 48 | 7 | 1 | 0 | 0 | 0 |

13 | ? | 319 | 27 | 1 | 0 | 0 | 0 |

14 | ? | 6623 | 161 | 2 | 0 | 0 | 0 |

15 | ? | ? | 934 | 1 | 0 | 0 | 0 |

16 | ? | ? | 7674 | 9 | 1 | 0 | 0 |

17 | ? | ? | 82240 | 53 | 0 | 0 | 0 |

18 | ? | ? | ? | 277 | 0 | 0 | 0 |

19 | ? | ? | ? | 1161 | 0 | 0 | 0 |

20 | ? | ? | ? | 7659 | 5 | 0 | 0 |

21 | ? | ? | ? | ? | 35 | 0 | 0 |

22 | ? | ? | ? | ? | ? | 1 | 0 |

23 | ? | ? | ? | ? | ? | 1 | 0 |

24 | ? | ? | ? | ? | ? | 5 | 0 |

[1] J. Goedgebeur, A. Neyt and C.T. Zamfirescu, Structural and computational results on platypus graphs, submitted, 2017. Preprint: arXiv:1712.05158