__Abstract__ In 1952 Sholander formulated an axiomatic characterization of the interval function of a tree with a … interval function of a block graph using axioms on an arbitrary transit function $R$. From this we deduce two new … characterizations of the interval function of a tree. …

A fundamental notion in metric graph theory is that of the interval function I : V × V → 2V – {} of a (finite … characterizing the interval function belongs to the central questions of metric graph theory, return here to this result again. In … studied extensively. Then the obstructions are pinpointed why such functions may not be the interval function of some …

A fundamental notion in metric graph theory is that of the interval function I : V × V → 2V – {∅} of a (finite … characterizing the interval function belongs to the central questions of metric graph theory, return here to this result again. In … studied extensively. Then the obstructions are pinpointed why such functions may not be the interval function of some …

, convexities and betweenness in graphs and posets. Prime examples of such transit functions are the interval function I and the …€˜transferring’ problems and ideas of one transit function to the other. For instance, a result on the interval function I might suggest … betweenness in graphs and posets. Prime examples of such transit functions are the interval function I and the induced path …

, convexities and betweenness in graphs and posets. Prime examples of such transit functions are the interval function I and the … ‘transferring’ problems and ideas of one transit function to the other. For instance, a result on the interval function I might …