Axiomatic characterization of the interval function of a block graph

In 1952 Sholander formulated an axiomatic characterization of the interval function of a tree with a partial proof. In 2011 Chvátal et al. gave a completion of this proof. In this paper we present a characterization of the interval function of a block graph using axioms on an arbitrary transit function RR. From this we deduce two new characterizations of the interval function of a tree.