  We study the presence of ferromagnetism in the phase diagram of the
two-dimensional honeycomb lattice close to half-filling (graphene) as a
function of the strength of the Coulomb interaction and doping. We show that
exchange interactions between Dirac fermions can stabilize a ferromagnetic
phase at low doping when the coupling is sufficiently large. In clean systems,
the zero temperature phase diagram shows both first order and second order
transition lines and two distinct ferromagnetic phases: one phase with only one
type of carriers (either electrons or holes) and another with two types of
carriers (electrons and holes). Using the coherent phase approximation (CPA) we
argue that disorder further stabilizes the ferromagnetic phase.
