Rotation snark, Berge-Fulkerson conjecture and Catlin’s 4-flow reduction

摘要

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. An infinite family R, of cyclically 5-edge-connected rotation snarks, was discovered in [European J. Combin. 2021] by Máčajová and Škoviera. In this paper, the Berge-Fulkerson conjecture is verified for the family R, and furthermore, a sup-family of R. Catlin’s contractible configuration and Tutte’s integer flow are applied here as the key methods.