It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. This conjecture has been verified for many families of snarks with small ($\le 5$) cyclic edge-connectivity. An infinite family, denoted by ${\mathcal{S}}_K$, of cyclically 6-edge-connected superposition snarks was constructed in [European J. Combin. 2002] by Kochol. In this paper, the Berge–Fulkerson conjecture is verified for the family ${\mathcal{S}}_K$, and, furthermore, some larger families containing ${\mathcal{S}}_K$. This is the first paper about the Berge–Fulkerson conjecture for superposition snarks and cyclically 6-edge-connected snarks. Tutte’s integer flow and Catlin’s contractible configuration are applied here as the key methods.

Berge和Fulkerson推测，每个无桥三次图都有六个完美匹配，因此每个边恰好包含在其中的两个中。这个猜想已经在许多带有小（$\le 5$）循环边缘连接性。一个无限的家庭，用${\mathcal{小号}}_{ķ}$，在[欧洲J. Combin。2002]。在本文中，Berge–Fulkerson猜想已针对该家族进行了验证${\mathcal{小号}}_{ķ}$，此外，还有一些较大的家庭，其中包括 ${\mathcal{小号}}_{ķ}$。这是有关叠加蛇和循环6边连接蛇的Berge-Fulkerson猜想的第一篇论文。Tutte的整数流和Catlin的可收缩配置在此处用作关键方法。