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We describe a factor-revealing convex optimization problem for theintegrality gap of the maximum-cut semidefinite programming relaxation: foreach $n \geq 2$ we present a convex optimization problem whose optimal value isthe largest possible ratio between the value of an optimal rank-$n$ solution tothe relaxation and the value of an optimal cut. This problem is then used tocompute lower bounds for the integrality gap.

On the integrality gap of the maximum-cut semidefinite programming relaxation in fixed dimension