On 0,±1 matrices, odd vectors, and bisubmodular polyhedra

In this note we describe a class of 0,±1 matrices A with the property that the system {Ay=c,y⩾0} has an integer solution y for each odd vector c provided that a rational solution exists. As a consequence, we obtain an integrality result on the dual of a certain maximization program over the intersection of two integer bisubmodular polyhedra.