Constructive characterizations for packing and covering with trees

Authors:
András Frank;László Szegö
Affiliations:
Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, Budapest, H-1117, Hungary and Ericsson Traffic Laboratory, Laborc u. 1. Budapest, ...;Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, Budapest, H-1117, Hungary
Venue:
Discrete Applied Mathematics - Submodularity
Year:
2003

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Abstract

We give a constructive characterization of undirected graphs which contain k spanning trees after adding any new edge. This is a generalization of a theorem of Henneberg and Laman who gave the characterization for k = 2. We also give a constructive characterization of graphs which have k edge-disjoint spanning trees after deleting any edge of them.