  We investigate the excitonic instability in the theory of Dirac fermions in
graphene with long-range Coulomb interaction. We analyze the electron-hole
vertex relevant for exciton condensation in the ladder approximation, showing
that it blows up at a critical value of the interaction strength \alpha =
e^2/4\pi v_F sensitive to further many-body corrections. Under static screening
of the interaction, we find that taking into account electron self-energy
corrections increases the critical coupling to \alpha_c \approx 2.09, for a
number N = 4 of two-component Dirac fermions. We show that the dynamical
screening of the interaction has however the opposite effect of enhancing the
instability, which turns out to develop then at \alpha_c \approx 0.99 for N =
4, bringing the question of whether that critical value can be reached by the
effective coupling in real graphene samples at the low-energy scales of the
exciton condensation.
