Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation

A recent claim that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson-Schwinger equations are taken to be bare. The running coupling is shown to be uniquely determined by the equations and to have a large finite infrared limit.