  We study the instability of the metallic state towards the formation of a new
ground state in graphene doped near the van Hove singularity. The system is
described by the Hubbard model and a field theoretical approach is used to
calculate the charge and spin susceptibility. We find that for repulsive
interactions, within the random phase approximation, there is a competition
between ferromagnetism and spin-density wave (SDW). It turns out that a SDW
with a triangular geometry is more favorable when the Hubbard parameter is
above the critical value U_c(T), which depends on the temperature T, even if
there are small variations in the doping. Our results can be verified by ARPES
or neutron scattering experiments in highly doped graphene.
