Defining rules in cost spanning tree problems through the canonical form

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.