Complexity results for the gap inequalities for the max-cut problem

We prove several complexity results about the gap inequalities for the max-cut problem, including (i) the gap-1 inequalities do not imply the other gap inequalities, unless NP= Co NP; (ii) there must exist non-redundant gap inequalities with exponentially large coefficients, unless NP= Co NP; (iii) the associated separation problem can be solved in finite (doubly exponential) time.