Highly connected hypergraphs containing no two edge-disjoint spanning connected subhypergraphs

摘要

We prove that there is no degree of connectivity which will guarantee that a hypergraph contains two edge-disjoint spanning connected subhypergraphs. We also show that Edmonds' theorem on arc-disjoint branchings cannot be extended to directed hypergraphs. Here we use a definition of a directed hypergraph that naturally generalizes the notion of a directed graph.