  Extensive computer simulations are performed for a few model glass-forming
liquids in both two and three dimensions to study their dynamics when a
randomly chosen fraction of particles are frozen in their equilibrium
positions. For all the studied systems, we find that the temperature-dependence
of the $\alpha$ relaxation time extracted from an overlap function related to
the self part of the density autocorrelation function can be explained within
the framework of the Random First Order Transition (RFOT) theory of the glass
transition. We propose a scaling description to rationalize the simulation
results and show that our data for the $\alpha$ relaxation time for all
temperatures and pin concentrations are consistent with this description. We
find that the fragility parameter obtained from fits of the temperature
dependence of the $\alpha$ relaxation time to the Vogel-Fulcher-Tammann (VFT)
form decreases by almost an order of magnitude as the pin concentration is
increased from zero. Our scaling description relates the fragility parameter to
the static length scale of RFOT and thus provides a physical understanding of
fragility within the framework of the RFOT theory. Implications of these
findings for the values of the exponents appearing in the RFOT theory are
discussed.
