Geodesic
Constructing hypohamiltonian snarks with cyclic connectivity 5 and 6
The electronic journal of combinatorics, Tome 14 (2007)
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A graph is hypohamiltonian if it is not hamiltonian but every vertex-deleted subgraph is. In this paper we study hypohamiltonian snarks – cubic hypohamiltonian graphs with chromatic index 4. We describe a method, based on superposition of snarks, which produces new hypohamiltonian snarks from old ones. By choosing suitable ingredients we can achieve that the resulting graphs are cyclically $5$-connected or $6$-connected. Previously, only three sporadic hypohamiltonian snarks with cyclic connectivity 5 had been found, while the flower snarks of Isaacs were the only known family of cyclically 6-connected hypohamiltonian snarks. Our method produces hypohamiltonian snarks with cyclic connectivity $5$ and $6$ for all but finitely many even orders.
DOI : 10.37236/936
Classification : 05C45, 05C40 
@article{10_37236_936,
     author = {Edita M\'a\v{c}ajov\'a and Martin \v{S}koviera},
     title = {Constructing hypohamiltonian snarks with cyclic connectivity 5 and 6},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/936},
     zbl = {1110.05057},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/936/}
}
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%J The electronic journal of combinatorics
%D 2007
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Edita Máčajová; Martin Škoviera. Constructing hypohamiltonian snarks with cyclic connectivity 5 and 6. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/936

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