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Loupekine Snarks

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LoupekineSnarks

The Loupekine snarks are the two snarks on 22 vertices and 33 edges illustrated above. They are implemented in the Wolfram Language as GraphData["LoupekineSnark1"] and GraphData["LoupekineSnark2"], respectively.

The second Loupekine snark has graph crossing number 5.

LoupekineSnarksCollier

The Loupekine snarks were found independently in the drawings shown above by Collier and Schmeichel (1978) who erroneously characterized them as "two new cubic hypohamiltonian graphs."

The Loupekine snarks are platypus graphs.

See also

Hypohamiltonian Graph, Snark

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References

Collier, J. B. and Schmeichel, E. F. "Systematic Searches for Hypohamiltonian Graphs." Networks 8, 193-200, 1978.Holton, D. A. and Sheehan, J. The Petersen Graph. Cambridge, England: Cambridge University Press, pp. 82 and 100-102, 1993.House of Graphs. Loupekine Snarks. Loupekines Snark 1 and Loupekines Snark 2.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 279, 1998.

Referenced on Wolfram|Alpha

Loupekine Snarks

Cite this as:

Weisstein, Eric W. "Loupekine Snarks." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LoupekineSnarks.html

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