On decomposing a hypergraph into k connected sub-hypergraphs

Authors:
András Frank;Tamás Király;Matthias Kriesell
Affiliations:
Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, Budapest, H-1117, Hungary and Traffic Lab Ericsson Hungary, Laborc u. 1, Budapest ...;Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, Budapest, H-1117, Hungary;Institut für Mathematics, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
Venue:
Discrete Applied Mathematics - Submodularity
Year:
2003

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Abstract

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 Tutte's 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.