On decomposing a hypergraph into k connected sub-hypergraphs Original Research Article

By applying the matroid partition theorem of J. Edmonds (J. Res. Nat. Bur. Standards Sect. B 69 (1965) 67) to a hypergraphic generalization of graphic matroids, due to Lorea (Cahiers Centre Etudes Rech. Oper. 17 (1975) 289), we obtain a generalization of Tutteʹs disjoint trees theorem for hypergraphs. As a corollary, we prove for positive integers k and q that every (kq)-edge-connected hypergraph of rank q can be decomposed into k connected sub-hypergraphs, a well-known result for q=2. Another by-product is a connectivity-type sufficient condition for the existence of k edge-disjoint Steiner trees in a bipartite graph.