It was recently proved by G Mazzuocolo (The Equivalence of Two Conjectures of Berge and Fulkerson, J. Graph Theory (2010) doi:10.1002/jgt.20545), that Berge-Fulkerson is indeed equivalent to the statement that for any 3-graph G, the edge-set of G can be covered by 5 perfect matchings. This might be worth mentioning it.

## equivalent conjecture

It was recently proved by G Mazzuocolo (The Equivalence of Two Conjectures of Berge and Fulkerson, J. Graph Theory (2010) doi:10.1002/jgt.20545), that Berge-Fulkerson is indeed equivalent to the statement that for any 3-graph G, the edge-set of G can be covered by 5 perfect matchings. This might be worth mentioning it.