  We study by extensive Monte Carlo simulations the effect of random bond
dilution on the phase transition of the three-dimensional 4-state Potts model
which is known to exhibit a strong first-order transition in the pure case. The
phase diagram in the dilution-temperature plane is determined from the peaks of
the susceptibility for sufficiently large system sizes. In the strongly
disordered regime, numerical evidence for softening to a second-order
transition induced by randomness is given. Here a large-scale finite-size
scaling analysis, made difficult due to strong crossover effects presumably
caused by the percolation fixed point, is performed.
