  Motivated by the possibility of superconductivity in doped graphene sheets,
we investigate superconducting order in the extended Hubbard model on the
two-dimensional graphene lattice using the variational cluster approximation
(VCA) and the cellular dynamical mean-field theory (CDMFT) with an exact
diagonalization solver at zero temperature. The nearest-neighbor interaction is
treated using a mean-field decoupling between clusters. We compare different
pairing symmetries, singlet and triplet, based on short-range pairing. VCA
simulations show that the real (nonchiral), triplet $p$-wave symmetry is
favored for small $V$, small on-site interaction $U$ or large doping, whereas
the chiral combination $p+ip$ is favored for larger values of $V$, stronger
on-site interaction $U$ or smaller doping. CDMFT simulations confirm the
stability of the $p+ip$ solution, even at half-filling. Singlet
superconductivity (extended $s$-wave or $d$-wave) is either absent or
sub-dominant.
