Minimum cost K-forest covers

A forest cover of a graph is a spanning forest for which each component has at least two nodes. If K is a subset of nodes, a K-forest cover is a forest cover including exactly one node from K in each component. A K-forest cover is of minimum cost if the sum of the costs of the edges is minimum. The authors present an algorithm for determining the minimum cost K-forest cover of a graph with n nodes. They show that the algorithm can also be used to determine, in time, the minimum cost K-forest cover having degree equal on each node v of an arbitrary subset of .