The equivalence of two conjectures of Berge and Fulkerson

Let G be a bridgeless cubic graph. Fulkerson conjectured that there exist six 1-factors of G such that each edge of G is contained in exactly two of them. Berge conjectured that the edge-set of G can be covered with at most five 1-factors. We prove that the two conjectures are equivalent. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:125-128, 2011 © 2011 Wiley Periodicals, Inc.