Edge-disjoint minimum-weight connected spanning k-edge subgraphs in a weighted graph: A connectedness theorem Original Research Article

Farber et al. (1985) proved that any pair of edge-disjoint spanning trees in a graph can be obtained from any other by a sequence of single-edge exchanges in a way that preserves, at each step, the property of being edge-disjoint spanning trees. In this paper, we consider a generalization of this problem concerning pairs of edge-disjoint minimum-weight connected spanning k-edge subgraphs in a weighted graph. It is shown that any pair of edge-disjoint minimum-weight connected spanning k-edge subgraphs of a weighted graph can be obtained from any other by a sequence of single-edge exchanges in a way that preserves, at each step, the property of being edge-disjoint minimum-weight connected spanning k-edge subgraphs. As an application, we give a two-dimensional interpolating theorem for some graphical invariants.