  The question of whether the Coulomb interaction is strong enough to break the
sublattice symmetry of un-doped graphene is discussed. We formulate a strong
coupling expansion where the ground state of the Coulomb Hamiltonian is found
exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We
argue that many of the properties of the resulting system would be shared by
graphene with a Hubbard model interaction. In particular, the best candidate
sublattice symmetry breaking ground state is an antiferromagnetic Mott
insulator. We discuss the results of some numerical simulations which indicate
that the Coulomb interaction is indeed subcritical. We also point out the
curious fact that, if the electron did not have spin degeneracy, the tendency
to break chiral symmetry would be much greater and even relatively weak Coulomb
interactions would likely gap the spectrum.
