Construction of Permutation Snarks

Abstract

A permutation snark is a snark which has a 2-factor $F_2$ consisting of two chordless circuits; $F_2$ is called the permutation 2-factor of $G$. We construct an infinite family $\mathcal{H}$ of cyclically 5-edge connected permutation snarks. Moreover, we prove for every member $G\in \mathcal{H}$ that the permutation 2-factor given by the construction of $G$ is not contained in any circuit double cover of $G$.