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In fact an inequality can always be replaced by another obtained by multiplying by a positive constant and adding any linear combination of the equations which define the affine space containing the polytope. Generally, full dimensional polytopes seem more pleasant to handle, so what is often done when studying the travelling salesman polytope is to consider, in fact, the SO called monotone trauelling salesman polytope: the convex hull of the incidence vectors of the hamilton cycles and all subsets of hamilton cycles of a graph.