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Cubic Hypohamiltonian Graph

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A cubic hypohamiltonian graph is a cubic graph that is also hypohamiltonian.

The numbers of cubic hypohamiltonian graphs on 2, 4, 6, ... vertices are 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 3, 1, 100, 52, 202, 304, ... (OEIS A305354; Goedgebeur and Zamfirescu 2017).

The following figure and table summarize small named cubic hypohamiltonian graphs.

CubicHypohamiltonianGraphs
vertex countcubic hypohamiltonian graphs
10Petersen graph
18(1,k)-Blanuša snarks
205-flower snark
22generalized Petersen graph GP(11,2), Loupekine snarks
2424-Thomassen graph
26(2,k)-Blanuša snarks, Celmins-Swart snarks
28Coxeter graph, 7-flower snark
30double star snark

See also

Cubic Graph, Cubic Planar Hypohamiltonian Graph, Hypohamiltonian Graph

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References

Goedgebeur, J. and Zamfirescu, C. T. "Improved Bounds for Hypohamiltonian Graphs." Ars Math. Contemp. 13, 235-257, 2017.House of Graphs. "Hypohamiltonian Graphs." https://houseofgraphs.org/meta-directory/hypohamiltonian.Sloane, N. J. A. Sequence A305354 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Cubic Hypohamiltonian Graph

Cite this as:

Weisstein, Eric W. "Cubic Hypohamiltonian Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CubicHypohamiltonianGraph.html

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