Antisymmetric flows and edge-connectivity

AbstractLet 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)∩−f(E)=∅. 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 Z33×Z66. 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