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

Abstract 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.

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