  We use the Gutzwiller method to investigate the importance of the on-site
Coulomb interaction in graphene. We apply it to Hubbard Hamiltonian to study
the renormalization of the kinetic energy in graphene due to the on-site
Coulomb interaction. We find that a reasonable strength of the interaction has
a very weak effect in reducing the kinetic energy. Hence we predict that the
Brinkmann-Rice metal-insulator transition in graphene is not possible. The
effect is understood in terms of the high kinetic energy in graphene.
