Maximum andk-th maximal spanning trees of a weighted graph

LetA be a maximum spanning tree andP be an arbitrary spanning tree of a connected weighted graphG. Then we prove that there exists a bijectionψ fromA/P intoP/A such that for any edgea∈A/P, (P/ψ(a)) ∪a is a spanning tree ofG whose weight is greater than or equal to that ofP. We apply this theorem to some problems concerning spanning trees of a weighted graph.