Partitioning a graph into alliance free sets

A strong defensive alliance in a graph G=(V,E) is a set of vertices A⊆V, for which every vertex v∈A has at least as many neighbors in A as in V−A. We call a partition A,B of vertices to be an alliance-free partition, if neither A nor B contains a strong defensive alliance as a subset. We prove that a connected graph G has an alliance-free partition exactly when G has a block that is other than an odd clique or an odd cycle.