Abstract: The effect of electron-impurity and electron-electron interactions on the energy spectrum of electrons moving in graphene is investigated in the presence of a high magnetic field. We find that the width of the broadened Landau levels exhibits an approximate 1/B dependence near half filling for charged impurity scattering. The Landau-level width, the density of states, and the Fermi energy exhibit an oscillatory behavior as a function of magnetic field. Comparison with experiment shows that scattering with charged impurities cannot be the main scattering mechanism that determines the width of the Landau levels.