EVERY N₂-LOCALLY CONNECTED CLAW-FREE GRAPH with MINIMUM DEGREE at LEAST 7 IS Z₃-CONNECTED

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 D(G) such that for every function b: V(G) → A satisfying ∑v ϵ V(G)b(v) = 0, there is a function f: E(G) →A∗such that for each vertex v ϵ 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). Let Z₃ denote the group of order 3. Jaeger et al. conjectured that there exists an integer k such that every k-edge-connected graph is Z₃-connected. In this paper, we prove that every N₂-locally connected claw-free graph G with minimum degree δ(G) ≥ 7 is Z₃-connected.