  We present the theory of many-body corrections to cyclotron transition
energies in graphene in strong magnetic field due to Coulomb interaction,
considered in terms of the renormalized Fermi velocity. A particular emphasis
is made on the recent experiments where detailed dependencies of this velocity
on the Landau level filling factor for individual transitions were measured.
Taking into account the many-body exchange, excitonic corrections and
interaction screening in the static random-phase approximation, we successfully
explained the main features of the experimental data, in particular that the
Fermi velocities have plateaus when the 0th Landau level is partially filled
and rapidly decrease at higher carrier densities due to enhancement of the
screening. We also explained the features of the nonmonotonous filling-factor
dependence of the Fermi velocity observed in the earlier cyclotron resonance
experiment with disordered graphene by taking into account the disorder-induced
Landau level broadening.
