A solution of Chartrand's problem on spanning trees (Q1062993)

It is proved that if a connected graph G contains two distinct spanning trees, then any two spanning trees of G can be connected by a chain of spanning trees, in which any two consecutive trees \(T_ i\) and \(T_{i+1}\) are adjacent, i.e., the symmetric difference \(E(T_ i)\Delta E(T_{i+1})\) consists of two adjacent edges.