When the Gomory–Chvátal closure coincides with the integer hull

Abstract Gomory–Chvatal cuts are prominent in integer programming. The Gomory–Chvatal closure of a polyhedron is the intersection of the half spaces defined by all its Gomory–Chvatal cuts. We prove that it is NP -hard to decide whether the Gomory–Chvatal closure of a rational polyhedron P is identical to the integer hull of P . An earlier version of this paper appeared in the proceedings of IPCO 2016.