Edge-connectivity and edge-disjoint spanning trees

where the minimum is taken over all subsets X of E(G) such that ω(G − X) − c > 0. In this paper, we establish a relationship 7 between λc(G) and τc−1(G), which gives a characterization of the edge-connectivity of a graph G in terms of the spanning tree 8 packing number of subgraphs of G. The digraph analogue is also obtained. The main results are applied to show that if a graph G is 9 s-hamiltonian, then L(G) is also s-hamiltonian, and that if a graph G is s-hamiltonian-connected, then L(G) is also s-hamiltonian10 connected. 11 c © 2007 Published by Elsevier B.V. 12