Abstract It is well known that the circular flow number of a bridgeless cubic graph can be computed in terms of certain partitions of its vertex set with prescribed properties. In the present paper, we first study some of these properties that turn out to be useful in order to make an efficient and practical implementation of an algorithm for the computation of the circular flow number of a bridgeless cubic graph. Using this procedure, we determine the circular flow number of all snarks on up to 36 vertices as well as the circular flow number of various famous snarks. After that, as combination of the use of this algorithm with new theoretical results, we present an infinite family of snarks of order 8 k + 2 whose circular flow numbers meet a general lower bound presented by Lukot’ka and Skoviera in 2008. In particular this answers a question proposed in their paper. Moreover, we improve the best known upper bound for the circular flow number of Goldberg snarks and we conjecture that this new upper bound is optimal.

中文翻译：

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snarks 循环流数的计算结果和新界限

摘要 众所周知，无桥三次图的循环流数可以根据其顶点集的具有指定属性的某些分区来计算。在本文中，我们首先研究了这些属性中的一些，这些属性被证明是有用的，以便有效和实用地实现计算无桥三次图的循环流数的算法。使用这个程序，我们确定了最多 36 个顶点上所有 snark 的循环流数以及各种著名的 snark 的循环流数。之后，结合使用该算法和新的理论结果，我们提出了 8 k + 2 阶 snarks 的无限族，其循环流数满足 Lukot'ka 和 Skoviera 在 2008 年提出的一般下界。特别是这回答了他们论文中提出的一个问题。此外，我们改进了 Goldberg snarks 循环流数的最著名的上限，我们推测这个新的上限是最优的。