Construction of Permutation Snarks
Jonas H\"agglund, Arthur Hoffmann-Ostenhof

TL;DR
This paper constructs an infinite family of cyclically 5-edge connected permutation snarks with a specific 2-factor property, and proves that this 2-factor is not contained in any circuit double cover, advancing understanding of snark structures.
Contribution
It introduces a new infinite family of permutation snarks with unique 2-factor properties and demonstrates their circuit double cover limitations.
Findings
Constructed an infinite family of cyclically 5-edge connected permutation snarks.
Proved the permutation 2-factor is not in any circuit double cover for these snarks.
Enhanced understanding of the structural properties of permutation snarks.
Abstract
A permutation snark is a snark which has a 2-factor consisting of two chordless circuits; is called the permutation 2-factor of . We construct an infinite family of cyclically 5-edge connected permutation snarks. Moreover, we prove for every member that the permutation 2-factor given by the construction of is not contained in any circuit double cover of .
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