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Platypus graphs

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.

Platypus graphs

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.

VerticesGirth ≥ 3Girth ≥ 4Girth ≥ 5Girth ≥ 6Girth ≥ 7Girth ≥ 8Girth ≥ 9
0-80000000
94000000
1048220000
11814430000
12248474871000
13?319271000
14?66231612000
15??9341000
16??76749100
17??8224053000
18???277000
19???1161000
20???7659500
21????3500
22?????10
23?????10
24?????50
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References

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


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