  We present a practical method for the solution of the quark-gluon vertex for
use in Bethe--Salpeter and Dyson--Schwinger calculations. The efficient
decomposition into the necessary covariants is detailed, with the numerical
algorithm outlined for both real and complex Euclidean momenta.
  A truncation of the quark-gluon vertex, that neglects explicit back-coupling
to enable the application to bound-state calculations, is given together with
results for the quark propagator and quark-gluon vertex for different quark
flavours. The relative impact of the various components of the quark-gluon
vertex is highlighted with the flavour dependence of the effective quark-gluon
interaction obtained, thus providing insight for the construction of
phenomenological models within Rainbow-Ladder. Finally, we solve the
corresponding Green's functions for complex Euclidean momenta as required in
future bound-state calculations.
