We study snarks whose edges cannot be covered by fewer than ve perfect matchings. Esperet and Mazzuoccolo found an innite family of such snarks, generalising an example provided by Hagglund. We construct another innite family, arising from a generalisation in a dierent 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 fow number C(G) > 5 and admit a 5-cycle double cover.
Tree-like snarks
ABREU, Marien;LABBATE, Domenico;
2016-01-01
Abstract
We study snarks whose edges cannot be covered by fewer than ve perfect matchings. Esperet and Mazzuoccolo found an innite family of such snarks, generalising an example provided by Hagglund. We construct another innite family, arising from a generalisation in a dierent 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 fow number C(G) > 5 and admit a 5-cycle double cover.File in questo prodotto:
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