  We investigate the influence of the full vacuum polarization and vertex
function on the fermion propagator, using the coupled Dyson--Schwinger
equations for the photon and fermion propagator. We show that, within a range
of vertex functions, the general behavior of the fermion propagator does not
depend on the exact details of the vertex, both in the massless and in the
massive phase. Independent of the precise vertex function, there is a critical
number of fermion flavors for dynamical mass generation in $(2+1)$-dimensional
QED. A consistent treatment of the vacuum polarization is essential for these
results.
