Geodesic
On hypohamiltonian snarks and a theorem of Fiorini
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 227-249.

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In 2003, Cavicchioli et al. corrected an omission in the statement and proof of Fiorini’s theorem from 1983 on hypohamiltonian snarks. However, their version of this theorem contains an unattainable condition for certain cases. We discuss and extend the results of Fiorini and Cavicchioli et al. and present a version of this theorem which is more general in several ways. Using Fiorini’s erroneous result, Steffen had shown that hypohamiltonian snarks exist for some orders n ≥ 10 and each even n ≥ 92. We rectify Steffen’s proof by providing a correct demonstration of a technical lemma on flower snarks, which might be of separate interest. We then strengthen Steffen’s theorem to the strongest possible form by determining all orders for which hypohamiltonian snarks exist. This also strengthens a result of Máčajová and Škoviera. Finally, we verify a conjecture of Steffen on hypohamiltonian snarks up to 36 vertices.
DOI : 10.26493/1855-3974.1176.9b7
Keywords: Hypohamiltonian, snark, irreducible snark, dot product 
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Jan Goedgebeur; Carol T. Zamfirescu. On hypohamiltonian snarks and a theorem of Fiorini. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 227-249. doi : 10.26493/1855-3974.1176.9b7. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1176.9b7/

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