Hypergraph connectivity augmentation

Abstract

The hypergraph augmentation problem is to augment a hypergraph by hyperedges to meet prescribed local connectivity requirements. We provide here a minimax theorem for this problem. The result is derived from the degree constrained version of the problem by a standard method. We shall construct the required hypergraph for the latter problem by a greedy type algorithm. A similar minimax result will be given for the problem of augmenting a hypergraph by weighted edges (hyperedges of size two with weights) to meet prescribed local connectivity requirements. Moreover, a special case of an earlier result of Schrijver on supermodular colourings shall be derived from our theorem.