Formulations and heuristics for minimal spanning trees with minimum degree constraints

Let G = (V, E) be a connected undirected graph, where V = {1, . . . , n} is the set of nodes and E the set of edges. Consider that there are associated positive costs, ce, to each edge e ∈ E. Given a positive integer valued function d : V → N on the nodes, the Min-Degree Constrained Minimum Spanning Tree (md-MST) problem consists in finding a spanning tree T of G with minimum total edge cost, given by ∑