Augmenting the Edge-Connectivity of a Hypergraph by Adding a Multipartite Graph


  • Supported by OTKA grants K60802 and CK80124.


Given a hypergraph, a partition of its vertex set, and a nonnegative integer k, find a minimum number of graph edges to be added between different members of the partition in order to make the hypergraph k-edge-connected. This problem is a common generalization of the following two problems: edge-connectivity augmentation of graphs with partition constraints (J. Bang-Jensen, H. Gabow, T. Jordán, Z. Szigeti, SIAM J Discrete Math 12(2) (1999), 160–207) and edge-connectivity augmentation of hypergraphs by adding graph edges (J. Bang-Jensen, B. Jackson, Math Program 84(3) (1999), 467–481). We give a min–max theorem for this problem, which implies the corresponding results on the above-mentioned problems, and our proof yields a polynomial algorithm to find the desired set of edges.