On the simultaneous edge-coloring conjecture

At the 16th British Combinatorial Conference (1997), Cameron introduced a new concept called 2-simultaneous edge-coloring and conjectured that every bipartite graphic sequence, with all degrees at least 2, has a 2-simultaneous edge-colorable realization. In fact, this conjecture is a reformulation of a conjecture of Keedwell (Graph Theory, Combinatorics, Algorithms and Applications, Proceedings of Third China–USA International Conference, Beijing, June 1–5, 1993, World Scientific Publ. Co., Singapore, 1994, pp. 111–124) on the existence of critical partial latin squares (CPLS) of a given type. In this paper, using some classical results about nowhere-zero 4-flows and oriented cycle double covers, we prove that this conjecture is true for all bipartite graphic sequences with all degrees at least 4.