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 Scienti c 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 4ows and oriented cycle double covers, we prove that this conjecture is true for all bipartite graphic sequences with all degrees at least 4. c © 2000 Elsevier Science B.V. All rights reserved.