= Let G be a connected undirected graph on n vertices. We say that two distinct spanning trees T and S of G are one swap away from each other if |TS| -2; that is, T and S differ in only one edge. For two distinct spanning trees T and S we say that R, R, ..., Rk form a swapping sequence from T to S if: 1. R = T, 2. Rk = S, and 3. for any 1 < i