Hypergraph connectivity augmentation

The hypergraph augmentation problem is to augment a hypergraph by hyperedge s to meet prescribed local connectivity requirements. We provide here a min imax theorem for this problem. The result is derived from the degree constr ained version of the problem by a standard method. We shall construct the r equired hypergraph for the latter problem by a greedy type algorithm. A sim ilar minimax result will be given for the problem of augmenting a hypergrap h by weighted edges (hyperedges of size two with weights) to meet prescribe d local connectivity requirements. Moreover, a special case of an earlier r esult of Schrijver on supermodular colourings shall be derived from our the orem.