1 Minimum Cost Bounded degree Spanning Tree

A natural generalization of minimum cost spanning tree is when we have some given degree bounds for each vertex and our goal is to find a minimum cost spanning tree statisfying the degree bounds. In other words, for a given graph G(V,E) and a bound Bv for each node v ∈ V , we want to find a spanning tree with minimum cost while degree of each v ∈ V is at most Bv (MCBDST). Note: This problem is NP-complete since if edge costs are all 1 and all degree bounds are 2 it is the Hamiltonian path problem. When all Bv’s are equal (say k) and the graph is unweighted, the problem is finding a spanning tree of maximum degree k.