TOTALLY UNIMODULAR LEONTIEF DIRECTED HYPERGRAPHS

A Leontief directed hypergraph is a generalization of a directed graph , where arcs have multiple (or no) tails and at most one head. We defi ne a class of Leontief directed hypergraphs via a forbidden structure called an odd pseudocycle. We show that the vertex-hyperarc incidence matrices of the hypergraphs in this class are totally unimodular. Inde ed, we show that this is the largest class with that property. We defi ne two natural subclasses of this class (one obtained by forbidding ps eudocycles and the other obtained by forbidding pseudocycles and the s o-called doublecycles), and we describe some structural properties of the bases and circuits of the members of these classes. We present exa mples of Leontief directed hypergraphs that are graphic, cographic, an d neither graphic nor cographic.