We characterize, in minimum cost spanning tree problems, the family of rules satisfying monotonicity over cost and population. We also prove that the set of allocations induced by the family coincides with the irreducible core.

The Boruvka's algorithm, which computes the minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature.