Lower Bound for the Number of Iterations in Semidefinite Hierarchies for the Cut Polytope

1.1. Preamble. Given a graph G = V E and a subset A ⊆ V , the cut determined by A is the vector A ∈ ±1 E with ijth entry −1 if and only if A∩ i j = 1. The cut polytope CUT G is the polytope in E defined as the convex hull of all cuts A (A⊆ V ). Given edge weights w ∈ E , the max-cut problem is the problem of finding a cut A whose weight ∑ ij∈E i∈A j ∈A wij is maximum. Hence, it can be formulated as the linear programming problem: