  We investigate the competition between electron-solid and quantum-liquid
phases in graphene, which arise in partially filled Landau levels. The
differences in the wave function describing the electrons in the presence of a
perpendicular magnetic field in graphene with respect to the conventional
semiconductors, such as GaAs, can be captured in a form factor which carries
the Landau level index. This leads to a quantitative difference in the
electron-solid and -liquid energies. For the lowest Landau level, there is no
difference in the wave function of relativistic and non-relativistic systems.
We compute the cohesive energy of the solid phase analytically using a
Hartree-Fock Hamiltonian. The liquid energies are computed analytically as well
as numerically, using exact diagonalization. We find that the liquid phase
dominates in the n=1 Landau level, whereas the Wigner crystal and
electron-bubble phases become more prominent in the n=2 and n=3 Landau level.
