  We report on single-cluster Monte Carlo simulations of the Ising, 4-state
Potts and 10-state Potts models on quenched ensembles of planar, tri-valent
random graphs. We confirm that the first-order phase transition of the 10-state
Potts model on regular 2D lattices is softened by the quenched connectivity
disorder represented by the random graphs and that the exponents of the Ising
and 4-state Potts models are altered from their regular lattice counterparts.
The behaviour of spin models on such graphs is thus more analogous to models
with quenched bond disorder than to Poisonnian random lattices, where regular
lattice critical behaviour persists.
  Using a wide variety of estimators we measure the critical exponents for all
three models, and compare the exponents with predictions derived from taking a
quenched limit in the KPZ formula for the Ising and 4-state Potts models.
Earlier simulations suggested that the measured values for the 10-state Potts
model were very close to the predicted quenched exponents of the {\it
four}-state Potts models. The analysis here, which employs a much greater range
of estimators and also benefits from greatly improved statistics, still
supports these numerical values.

High Energy Physics - Lattice;Statistical Mechanics;General Relativity and Quantum Cosmology