  The quadratic assignment problem is a well-known optimization problem with
numerous applications. A common strategy to solve it is to use one of its
linearizations and then apply the toolbox of mixed integer linear programming
methods. One measure of quality of a mixed integer formulation is the quality
of its linear relaxation. In this paper, we compare two linearizations of the
quadratic assignment problem and prove that the linear relaxation of the
linearization of Adams and Johnson is contained in the linear relaxation of the
linearization of Xia and Yuan. We furthermore develop a Branch and Cut approach
using the insights obtained in the proof that enhances the linearization of Xia
and Yuan via a new family of cuts called ab-cuts.
