Let G = (U, V, E) be a bipartite graph with weights of its edges cij. For the assignment and transportation problem given by such a graph we propose efficient procedures for partitioning the edge set E into three classes: E0 is the set of edges ij with xij = 0 for each optimum solution (0-persistent edges); E1 is the set of edges with xij > 0 and constant for each optimum (1-persistent edges) and Ew is the set of edges such that there are two optimum solutions x, x′ with xij ≠ x′ij (weakly persistent edges).
