Characterization of the Distance between Subtrees of a Tree by the Associated Tight Span

Abstract.

A characterization is given to the distance between subtrees of a tree defined as the shortest path length between subtrees. This is a generalization of the four-point condition for tree metrics. For this, we use the theory of the tight span and obtain an extension of the famous result by Dress that a metric is a tree metric if and only if its tight span is a tree.