Let G = (V,A,g) be a strongly connected weighted graph. We say that G is max-balanced if for every cut W, the maximum weight over arcs leaving W equals the maximum weight over arcs entering W. A subgraph H of G is max-sufficient if (or every cut W, the maximum weight over a.rcs of G leaving W is attained at some arc of H. A tower T = (CI,C., ... ,C,) is a sequence of arc-sets of G where C'+ I is a cycle all of whose weights are maximal in the graph formed by contracting the sets CI , C… CONTINUE READING