  We have implemented a generic method, based on the 2n+1 theorem within
density functional perturbation theory, to calculate the anharmonic scattering
coefficients among three phonons with arbitrary wavevectors. The method is used
to study the phonon broadening in graphite and graphene mono- and bi-layer. The
broadening of the high-energy optical branches is highly nonuniform and
presents a series of sudden steps and spikes. At finite temperature, the two
linearly dispersive acoustic branches TA and LA of graphene have nonzero
broadening for small wavevectors. The broadening in graphite and bi-layer
graphene is, overall, very similar to the graphene one, the most remarkable
feature being the broadening of the quasi acoustical ZO' branch. Finally, we
study the intrinsic anharmonic contribution to the thermal conductivity of the
three systems, within the single mode relaxation time approximation. We find
the conductance to be in good agreement with experimental data for the
out-of-plane direction but to underestimate it by a factor 2 in-plane.
