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

Authors:
Jørgen Bang-Jensen;Stéphan Thomassé
Affiliations:
Department of Mathematics and Computer Science, University of Southern Denmark, Odense DK-5230, Denmark;LaPCS, Université Claude Bernard, Lyon 1, France
Venue:
Discrete Applied Mathematics - Submodularity
Year:
2003

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Abstract

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.