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.
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