I discuss possible realization, in doped graphene monolayer,  of a  chiral superconductivity which breaks time-reversal symmetry,  and exotic  spin-density-wave (SDW) order which preserves full Fermi surface.  A unique situation arises in graphene at the critical doping where the Fermi surface is nested and the density of states is singular. In this regime, d-wave superconductivity and SDW order   emerge from repulsive electron-electron interactions. Using a renormalization group method, I show that superconductivity wins at the critical doping, but SDW wins at slightly smaller or slightly larger doping. Superconductivity develops simultaneously in two degenerate d-wave pairing channels and   is of chiral type, with the phase of the superconducting order parameter winding by 4 around the Fermi surface.  Such a state breaks the time reversal symmetry and exhibit many other fascinating properties.   SDW state is uniaxial, with order parameter breaking  O(3) * Z4 symmetry.  I show that this SDW state is a    half-metal – excitations in one spin branch are gapped, but excitations in the other spin branch remain gapless and preserve full original Fermi surface. Such a state is highly desirable for nano-science as it allows for electrical control of spin currents.