  We give an incremental polynomial time algorithm for enumerating the vertices
of any polyhedron $\mathcal{P}(A,\mathbf{1})=\{x\in\RR^n \mid Ax\geq \b1,~x\geq
\b0\}$, when $A$ is a totally unimodular matrix. Our algorithm is based on
decomposing the hypergraph transversal problem for unimodular hypergraphs using
Seymour's decomposition of totally unimodular matrices, and may be of
independent interest.
