Z₃-connectivity in Abelian Cayley graphs

Let G be a 2-edge-connected undirected graph, A be an (additive) Abelian group and A = A - {0}. A graph G is A-connected if G has an orientation G such that for every map b : V(G) → A satisfying v V(G) b(v) = 0, there is a function f : E(G) → Asuch that for each vertex v V(G), the total amount of f -values on the edges directed out from v minus the total amount of f -values on the edges directed into v equals b(v). Jaeger et al. [F. Jaeger, N. Linial, C. Payan, M. Tarsi, Group connectivity of graphs-a nonhomogeneous analogue of nowhere-zero flow properties, J. Combinatorial Theory, Series B 56 (1992) 165-182] conjectured that every 5-edge-connected graph G is Z ₃-connected, where Z3 is the cyclic group of order 3. In this paper we prove that every connected Cayley graph G of degree at least 5 on an Abelian group is Z₃-connected.