  We study, by means of a Monte Carlo simulator, the hot phonon effect on the
relaxation dynamics in photoexcited graphene and its quantitative impact as
compared to considering an equilibrium phonon distribution. Our multi-particle
approach indicates that neglecting the hot phonon effect significantly
underestimates the relaxation times in photoexcited graphene. The hot phonon
effect is more important for a higher energy of the excitation pulse and
photocarrier densities between $1$ and $3\times 10^{12} \mathrm{~cm}^{-2}$.
Acoustic intervalley phonons play a non-negligible role, and emitted phonons
with wavelengths limited up by a maximum (determined by the carrier
concentration) induce a slower carrier cooling rate. Intrinsic phonon heating
is damped in graphene on a substrate due to additional cooling pathways, with
the hot phonon effect showing a strong inverse dependence with the carrier
density.
