We present an algorithm for the efficient generation of all pairwise non-isomorphic cycle permutation graphs, i.e. cubic graphs with a $2$-factor consisting of two chordless cycles, non-hamiltonian cycle permutation graphs and permutation snarks, i.e. cycle permutation graphs that do not admit a $3$-edge-colouring. This allows us to generate all cycle permutation graphs up to order $34$ and all permutation snarks up to order $46$, improving upon previous computational results by Brinkmann et al. Moreover, we give several improved lower bounds for interesting permutation snarks, such as for a smallest permutation snark of order $6 \bmod 8$ or a smallest permutation snark of girth at least $6$ and give more evidence in support of a conjecture of Goddyn. These computational results also allow us to complete a characterisation of the orders for which non-hamiltonian cycle permutation graphs exist, answering an open question by Klee from 1972, and yield many more counterexamples to conjectures by Jackson and Zhang.

翻译：我们提出了一种高效生成所有两两非同构的循环置换图的算法，即包含由两个无弦环组成的2-因子的三次图、非哈密顿循环置换图，以及置换斯纳克图（即不允许3-边着色的循环置换图）。该算法允许我们生成所有阶数不超过34的循环置换图，以及所有阶数不超过46的置换斯纳克图，改进了Brinkmann等人之前的研究结果。此外，我们为有趣的置换斯纳克图（例如阶数为6 mod 8的最小置换斯纳克图或围长至少为6的最小置换斯纳克图）给出了几个改进的下界，并为支持Goddyn猜想提供了更多证据。这些计算结果还使我们能够完成非哈密顿循环置换图存在阶数的刻画，回答了Klee于1972年提出的一个开放问题，并为Jackson和Zhang的猜想提供了更多反例。