  We present a first-principles study of the electron-phonon (e-ph)
interactions and their contributions to the linewidths for the optical phonon
modes at $\Gamma$ and K in one to three-layer graphene. It is found that due to
the interlayer coupling and the stacking geometry, the high-frequency optical
phonon modes in few-layer graphene couple with different valence and conduction
bands, giving rise to different e-ph interaction strengths for these modes.
Some of the multilayer optical modes derived from the $\Gamma$-$E_{2g}$ mode of
monolayer graphene exhibit slightly higher frequencies and much reduced
linewidths. In addition, the linewidths of K-$A'_1$ related modes in
multilayers depend on the stacking pattern and decrease with increasing layer
numbers.
