Cost additive rules in minimum cost spanning tree problems with multiple sources

In this paper, we introduce a family of rules in minimum cost spanning tree problems with multiple sources called Kruskal sharing rules. This family is characterized by cone-wise additivity and independence of irrelevant trees. We also investigate some subsets of this family and provide axiomatic characterizations of them. The first subset is obtained by adding core selection. The second is obtained by adding core selection and equal treatment of source costs.