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K2-hypohamiltonian graphs

A K2-hypohamiltonian graph is a non-hamiltonian graph in which the removal of any pair of adjacent vertices yields a hamiltonian graph.

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

The following lists are available:

Lists of hypohamiltonian graphs can be found here.

K2-hypohamiltonian graphs

The following table gives the complete lists of all K2-hypohamiltonian graphs with a given lower bound on the girth.

All results were obtained with the program GenK2Hypohamiltonian , see [1,2] for details.

VerticesGirth ≥ 3Girth ≥ 4Girth ≥ 5Girth ≥ 6Girth ≥ 7
1011100
1100000
1200000
1311100
1400000
1511100
1644400
1700000
1833300
1928282800
20?2200
21??3100
22??33200
23??1900
24??61300
25???10
26???00
27???00
28-30????0
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K2-hypohamiltonian snarks

Lists of K2-hypohamiltonian snarks can be found on the snarks page.


References

[1] J. Goedgebeur, J. Renders, G. Wiener and C.T. Zamfirescu, K2-Hamiltonian Graphs: II, manuscript.

[2] J. Goedgebeur, J. Renders, and C.T. Zamfirescu, Generation and new infinite families of K2-hypohamiltonian graphs, manuscript.


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