Geodesic
Treelike snarks
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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We study snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hägglund. We construct another infinite family, arising from a generalisation in a different direction. The proof that this family has the requested property is computer-assisted. In addition, we prove that the snarks from this family (we call them treelike snarks) have circular flow number $\phi_C (G)\ge5$ and admit a 5-cycle double cover.
DOI : 10.37236/6008
Classification : 05C15, 05C70
Mots-clés : snarks, excessive index, circular flow number 
@article{10_37236_6008,
     author = {Mari\'en Abreu and Tom\'a\v{s} Kaiser and Domenico Labbate and Giuseppe Mazzuoccolo},
     title = {Treelike snarks},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {3},
     doi = {10.37236/6008},
     zbl = {1351.05068},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6008/}
}
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Marién Abreu; Tomáš Kaiser; Domenico Labbate; Giuseppe Mazzuoccolo. Treelike snarks. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/6008

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