Matrices with the Edmonds - Johnson property

A matrix A = (a~j) has the Edmonds--Johnson property if, for each choice of integral vectors dl, d,., b~, b~, the convex hull of the integral solutions of dt~-x~-d2, bt~-Ax~-b.~ is obtained by adding the inequalities cx~_[~], where c is an integral vector and cx~_J holds for each solution of da~_x~_d2, b~_Ax~_b.. We characterize the Edmonds--Johnson property for integral matrices A which satisfy S la~j[-~2 for each (row index) i. A corollary is that if G is an undirected 1 graph which does not contain any hom~omorph of / (4 in which all triangles of/(4 have become odd circuits, then G is t-perfect. This extends results of Boulala, Fonlupt, Sbihi and Uhry.