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, and non-hamiltonian cycle permutation graphs, from which the permutation snarks can easily be computed. 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 $6$. 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 a conjecture by Zhang.

翻译：本文提出一种高效生成所有两两不同构的循环置换图（即具有由两个无弦环构成的$2$-因子的三次图）及非哈密顿循环置换图的算法，并基于此可简便计算出置换蛇图。该算法使我们能够生成所有阶数不超过$34$的循环置换图及所有阶数不超过$46$的置换蛇图，从而改进了Brinkmann等人先前的研究成果。此外，我们针对若干具有理论意义的置换蛇图给出了改进的下界估计，例如关于阶数为$6 \bmod 8$的最小置换蛇图以及围长至少为$6$的最小置换蛇图。这些计算结果不仅帮助我们完整刻画了非哈密顿循环置换图存在的阶数特征，从而解决了Klee于1972年提出的公开问题，还为Zhang猜想提供了更多反例。