On the Submodular Matrix Representation of a Digraph

We reexamine the class of (0,+-1) matrices called submodular,
which we introduced in [2]. Our key idea in this paper is to define, for each
submodular matrix M, a corresponding digraph G whose nodes are the columns of
M. Our principal results are: (a) a graph-theoretic interpretation of the polyhedron
P(M) = {x : x >= 0,M >= -l},and (b) for a given G, the description of a submodular
matrix contained in all submodular matrices representing G.