  We formulate the spin foam perturbation theory for three-dimensional
Euclidean Quantum Gravity with a cosmological constant. We analyse the
perturbative expansion of the partition function in the dilute-gas limit and we
argue that the Baez conjecture stating that the number of possible distinct
topological classes of perturbative configurations is finite for the set of all
triangulations of a manifold, is not true. However, the conjecture is true for
a special class of triangulations which are based on subdivisions of certain
3-manifold cubulations. In this case we calculate the partition function and
show that the dilute-gas correction vanishes for the simplest choice of the
volume operator. By slightly modifying the dilute-gas limit, we obtain a
nonvanishing correction which is related to the second order perturbative
correction. By assuming that the dilute-gas limit coupling constant is a
function of the cosmological constant, we obtain a value for the partition
function which is independent of the choice of the volume operator.
