Covering symmetric supermodular functions by uniform hypergraphs

Abstract

We consider the problem of finding a uniform hypergraph that satisfies cut demands defined by a symmetric crossing supermodular set function. We give min–max formulas for both the degree specified and the minimum cardinality problem. These results include as a special case a formula on the minimum number of r-hyperedges whose addition to an initial hypergraph will make it k-edge-connected.