Representations of chordal graphs as subtrees of a tree

In 1974, Buneman [ l ] and Gavril [2] independently showed that a connected graph G is isomorphic to the intersection graph of subtrees of a tree if and only if G is chordal. This result, which also appears in [5] , can be derived directly from a result of Lekkerkerker and Boland [4] , which states that a chordal graph has a simplicia1 point. We give a proof of this characterization and we conclude with an announcement of a criterion for a graph to be representable on Kl,3. In general, we follow the graph theoretic terminology of [3] .