  We show that any planar drawing of a forest of three stars whose vertices are
constrained to be at fixed vertex locations may require $\Omega(n^\frac{2}{3})$
edges each having $\Omega(n^\frac{1}{3})$ bends in the worst case. The lower
bound holds even when the function that maps vertices to points is not a
bijection but it is defined by a 3-coloring. In contrast, a constant number of
bends per edge can be obtained for 3-colored paths and for 3-colored
caterpillars whose leaves all have the same color. Such results answer to a
long standing open problem.
