  The spectrum of electron-phonon complexes in a monolayer graphene is
investigated in the presence of a perpendicular quantizing magnetic field.
Despite the small electron-phonon coupling, usual perturbation theory is
inapplicable for calculation of the scattering amplitude near the threshold of
the optical phonon emission. Our findings beyond perturbation theory show that
the true spectrum near the phonon emission threshold is completely governed by
new branches, corresponding to bound states of an electron and an optical
phonon with a binding energy of the order of $\alpha \omega_{0}$ where $\alpha$
is the electron-phonon coupling and $\omega_{0}$ the phonon energy.
