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.

Minimum-cost spanning tree problems are well-known problems in the operations research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused,...