  We develop a composite Dirac fermion theory for the fractional quantum Hall
effects (QHE) near charge neutrality in graphene. We show that the interactions
between the composite Dirac fermions lead to dynamical mass generation through
exciton condensation. The four-fold spin-valley degeneracy is fully lifted due
to the mass generation and the exchange effects such that the odd-denominator
fractional QHE observed in the vicinity of charge neutrality can be understood
in terms of the integer QHE of the composite Dirac fermions. At the filling
factor $\nu=1/2$, we show that the massive composite Dirac fermion liquid is
unstable against chiral p-wave pairing for weak Coulomb interactions and the
ground state is a paired nonabelian state described by the Moore-Read Pfaffian
in the long wavelength limit.
