In this paper, the authors consider inequalities of the form Σαjxj≥β, where αj equals 0 or 1, and β is a positive integer. They give necessary and sufficient conditions for such inequalities to define facets of the set covering polytope associated with a 0,1 constraint matrix A. These conditions are in terms of critical edges and critical cutsets defined in the bipartite incidence graph of A, and are in the spirit of the work of the Balas and Zemel on the set packing problem where similar notions were defined in the intersection graph of A. Furthermore, the authors give a polynomial characterization of a class of 0,1 facets defined from chorded cycles of the bipartite incidence graph. This characterization also yields all the 0,1 liftings of odd-hole inequalities for the simple plant location polytope.
