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.
The following table gives the complete lists of all platypus graphs with a given lower bound on the girth.
All results were obtained with the program GenHypohamiltonian , see [1] for details.
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