  The Dyson-Schwinger quark equation is solved for the quark-gluon vertex using
the most recent lattice data available in the Landau gauge for the quark, gluon
and ghost propagators, the full set of longitudinal tensor structures in the
Ball-Chiu vertex, taking into account a recently derived normalisation for a
quark-ghost kernel form factors and the gluon contribution for the tree level
quark-gluon vertex identified on a recent study of the lattice soft gluon
limit. A solution for the inverse problem is computed after the Tikhonov linear
regularisation of the integral equation, that implies solving a modified
Dyson-Schwinger equation. We get longitudinal form factors that are strongly
enhanced at the infrared region, deviate significantly from the tree level
results for quark and gluon momentum below 2 GeV and at higher momentum
approach their perturbative values. The computed quark-gluon vertex favours
kinematical configurations where the quark momentum $p$ and the gluon momentum
$q$ are small and parallel. Further, the quark-gluon vertex is dominated by the
form factors associated to the tree level vertex $\gamma_\mu$ and to the
operator $2 \, p_\mu + q_\mu$. The higher rank tensor structures provide small
contributions to the vertex.
