2-Change for k-connected networks

The authors consider the problem of designing a k-connected network at minimum weight. They show that a 2-change transformation can always be applied when k is even. As a result, for k even, no two edges of a minimum weight k-connected network are crossing when the vertices are points in the Euclidean plane. A similar result for a linear programming relaxation of this network design problem is shown to be valid for all k.