md-MST is NP-hard for d≥3

Let G=(V,E) be a connected weighted undirected graph. Given a positive integer d, the Min-Degree Constrained Minimum Spanning Tree (md-MST) problem consists in finding a spanning tree T for G having minimum total edge cost and such as each node i in the tree either has degree at least d or is a leaf node. In the present work we prove that this recently introduced combinatorial problem is NP-hard in general.