Antisymmetric flows and edge-connectivity

Let G = (V, E) be a directed graph, let M be an abelian group, and let f : E --> M be a flow. We say that f is antisymmetric if f (E) boolean AND - f (E) = circle divide. Using a theorem of DeVos, Johnson, and Seymour, we improve upon a result of theirs by showing that every directed graph (without the obvious obstruction) has an antisymmetric flow in the group Z(3)(3) x Z(6)(6). We also provide some additional theorems proving the existence of an antisymmetric flow in a smaller group, under the added assumption that G has a certain edge-connectivity. (C) 2003 Elsevier B.V. All rights reserved.