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A note on packing spanning trees in graphs and bases in matroids. (English) Zbl 1296.05103
Summary: We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We provide descriptions of such graphs and matroids, showing that such a graph (or matroid) has a unique decomposition. In the case of graphs, our results are relevant for certain communication protocols.

MSC:
05C40 Connectivity
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05B35 Combinatorial aspects of matroids and geometric lattices
05C90 Applications of graph theory
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