Characterizing rules in minimum cost spanning tree problems

A theorem of Bergantiños and Vidal-Puga (2015) states that in minimum cost spanning tree problems a rule satisfies separability and reductionism if and only if it is induced by an extra-costs function. In this article, we point out that the positivity of the extra-costs function implies the positivity of the rule; moreover, we prove that the rule further satisfies continuity if and only if the extra-costs function is continuous, and it satisfies symmetry if and only if the extra-costs function is symmetric.