In the well-solved edge-connectivity augmentation problem, a minimum cardinality set F of edges to add to a given undirected graph to make it k-connected should be found. The generalization where every edge of F must go between two different sets of a given partition of the vertex set is solved. A special case of this partition-constrained problem increases the edge-connectivity of a bipartite graph to k while preserving bipartiteness. Based on this special case, an application of the results in statics is presented. The solution to the general partition-constrained problem gives a min-max formula for |F| which includes as a special case the original min-max formula for the problem without partition constraints.
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