Berge–Fulkerson coloring for C(12)‐linked permutation graphs

Abstract

AbstractIt 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. Let be a permutation graph with a 2‐factor . A circuit is ‐alternating if is a perfect matching of . A permutation graph with a 2‐factor is ‐linked if it contains an ‐alternating circuit of length at most 12. It is proved in this paper that every‐linked permutation graph is Berge–Fulkerson colorable. As an application, the conjecture is verified for some families of snarks constructed by Abreu et al., Brinkmann et al., and Hägglund et al.