Matrices with the edmonds—Johnson property

AbstractA matrixA=(aij) has theEdmonds—Johnson property if, for each choice of integral vectorsd1,d2,b1,b2, the convex hull of the integral solutions ofd1≦x≦d2,b1≦Ax≦b2 is obtained by adding the inequalitiescx≦|δ|, wherec is an integral vector andcx≦δ holds for each solution ofd1≦x≦d2,b1≦Ax≦b2. We characterize the Edmonds—Johnson property for integral matricesA which satisfy $$\mathop \Sigma \limits_j |a_{ij} | \leqq 2$$ for each (row index)i. A corollary is that ifG is an undirected graph which does not contain any homeomorph ofK4 in which all triangles ofK4 have become odd circuits, thenG ist-perfect. This extends results of Boulala, Fonlupt, Sbihi and Uhry.