  The linewidths of the electronic bands originating from the electron-phonon
coupling in graphene are analyzed based on model tight-binding calculations and
experimental angle-resolved photoemission spectroscopy (ARPES) data. Our
calculations confirm the prediction that the high-energy optical phonons
provide the most essential contribution to the phonon-induced linewidth of the
two upper occupied $\sigma$ bands near the $\bar{\Gamma}$-point. For larger
binding energies of these bands, as well as for the $\pi$ band, we find
evidence for a substantial lifetime broadening from interband scattering $\pi
\rightarrow \sigma$ and $\sigma \rightarrow \pi$, respectively, driven by the
out-of-plane ZA acoustic phonons. The essential features of the calculated
$\sigma$ band linewidths are in agreement with recent published ARPES data [F.
Mazzola et al., Phys.~Rev.~B. 95, 075430 (2017)] and of the $\pi$ band
linewidth with ARPES data presented here.
