Many-body effects resulting from strong electron-electron and electron-phonon interactions play a significant role in graphene physics. We report on their manifestation in low B field magneto-phonon resonances in high quality exfoliated single-layer and bilayer graphene encapsulated in hexagonal boron nitride. These resonances allow us to extract characteristic effective Fermi velocities, as high as $1.20 times 10^6$ m/s, for the observed dressed Landau level transitions, as well as the broadening of the resonances, which increases with Landau level index.
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