In this paper, some earlier results by Fleischner [H. Fleischner, Bipartizing matchings and Sabidussi’s compatibility conjecture, DiscreteMath. 244 (2002) 77–82] about edge-disjoint bipartizingmatchings of a cubic graphwith a dominating circuit are generalized for graphs without the assumption of the existence of a dominating circuit and 3-regularity. A pair of integer flows (D, f1) and (D, f2)...