Minimally Infeasible Set-Partitioning Problems with Balanced Constraints

We study properties of systems of linear constraints that are minimally infeasible with respect to some subset S of constraints (i.e. systems that are infeasible, but become feasible upon removal of any constraint in S). We then apply these results and a theorem of Conforti, Cornuéjols, Kapoor, and Vušković, to a class of 0, 1 matrices, for which the linear relaxation of the set partitioning polytope LSP (A) = {x |Ax = 1, x ≥ 0} is integral. In this way we obtain combinatorial properties of those matrices in the class that are minimal (w.r.t. taking row submatrices) with the property that the set partitioning polytope associated with them is infeasible.