  In 1992, Kalai and Kleitman proved the first subexponential upper bound for
the diameters of convex polyhedra. Eisenbrand et al. proved this bound holds
for connected layer families, a novel approach to analyzing polytope diameters.
Very recently, Todd improved the Kalai-Kleitman bound for polyhedra to
$(n-d)^{1+\log_2d}$. In this note, we prove an analogous upper bound on the
diameters of subset partition graphs satisfying a property related to the
connectivity property of connected layer families.
