  We study the superconducting phases of the two-dimensional honeycomb lattice
of graphene. We find two spin singlet pairing states, s-wave and an exotic
$p+ip$ that is possible because of the special structure of the honeycomb
lattice. At half filling, the $p+ip$ phase is gapless and superconductivity is
a hidden order. We discuss the possibility of a superconducting state in metal
coated graphene.
