  We consider the running coupling from the four-gluon vertex in Landau gauge,
SU($N_c$) Yang-Mills theory as given by a combination of dressing functions of
the vertex and the gluon propagator. We determine these functions numerically
from a coupled set of Dyson-Schwinger equations. We reproduce asymptotic
freedom in the ultraviolet momentum region and find a coupling of order one at
mid-momenta. In the infrared we find a nontrivial (i.e. nonzero) fixed point
which is three orders of magnitude smaller than the corresponding fixed point
in the coupling of the ghost-gluon vertex. This result explains why the
Dyson-Schwinger and the functional renormalization group equations for the two
point functions can agree in the infrared, although their structure is quite
different. Our findings also support Zwanziger's notion of an infrared
effective theory driven by the Faddeev-Popov determinant.
