A characterization of box $1/d$-integral binary clutters

Let Q6 denote the port of the dual Fano matroid F*7 and let Q7 denote the clutter consisting of the circuits of the Fano matroid F7 that contain a given element. Let be a binary clutter on E and let d = 2 be an integer. We prove that all the vertices of the polytope {x E+ | x(C) = 1 for C } n {x | a = x = b} are -integral, for any -integral a, b, if and only if does not have Q6 or Q7 as a minor. This includes the class of ports of regular matroids. Applications to graphs are presented, extending a result from Laurent and Pojiak [7].