  The cut dominant of a graph is the unbounded polyhedron whose points are all
those that dominate some convex combination of proper cuts. Minimizing a
nonnegative linear function over the cut dominant is equivalent to finding a
minimum weight cut in the graph. We give a forbidden-minor characterization of
the graphs whose cut dominant can be defined by inequalities with integer
coefficients and right-hand side at most 2. Our result is related to the
forbidden-minor characterization of TSP-perfect graphs by Fonlupt and Naddef
(Math. Prog., 1992). We prove that our result implies theirs, with a shorter
proof. Furthermore, we establish general properties of forbidden minors for
right-hand sides larger than 2.
