Treelike Snarks

  • Marién Abreu
  • Tomáš Kaiser
  • Domenico Labbate
  • Giuseppe Mazzuoccolo
Keywords: Snarks, Excessive index, Circular flow number


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.
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