  The quark propagator is studied under a truncation scheme beyond the rainbow
approximation by dressing the quark-gluon vertex non-perturbatively. It is
found that, in the chiral limit with dynamical symmetry breaking, the dynamical
quark mass and the quark condensate are significantly enhanced due to the
non-Abelian contribution arising from the three-gluon interaction compared to
those under the rainbow approximation; and the critical strength of the
dynamical chiral symmetry breaking is much lowered. The Abelian contribution is
much smaller than the non-Abelian contribution. A technical issue on removing
the ultraviolet divergences including the overlapping divergences is discussed.
