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Treelike snarks

Research paper by Marién Abreu, Tomas Kaiser, Domenico Labbate, Giuseppe Mazzuoccolo

Indexed on: 05 Jan '16Published on: 05 Jan '16Published in: Mathematics - Combinatorics



Abstract

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 Hagglund. 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 five and admit a 5-cycle double cover.