The spanning tree packing number of a graph G, denoted σ(G), is the largest number of edge-disjoint spanning trees in G. An obvious upper bound on σ(G) is the edge-connectivity of G. We consider those graphs for which these two parameters are equal, and obtain a constructive description of them. We can also ask an equivalent question for matroids, and will conclude by mentioning this.
This is joint work with Brett Stevens (Carleton) and Mike Newman (Ottawa).