Strong branchwidth and local transversals

We consider representations of chordal graphs as edge intersection graphs of subtrees in a tree of maximum vertex degree 3. A new graph invariant related to the concept of branchwidth is introduced, and a structural characterization theorem is given for the existence of representations where each edge is contained in fewer subtrees than the clique number of the graph represented. As a consequence, a sufficient condition is obtained for chordal graphs to have smaller branchwidth than clique number.