  We propose a graphene-based model for realizing a new type of gapless
condensate by pairing of electron-like (n) carriers of a Dirac cone conduction
band with hole-like (p) carriers of a Dirac valance band. Ferromagnetic
superconductivity (FS) in monolayer graphene or pairing between oppositely (n
and p) doped layers of a double layer graphene allow for the formation of this
p-n superconductivity. For FS in graphene, the p-n condensate dominates the
zero temperature phase diagram at low levels of doping and high exchange
fields. We show that p-n pairing with p+ip-wave symmetry presents a stable
condensate phase, which can cover the phase diagram up to surprisingly strong
exchange fields. Our study reveals that the characteristics of relativistic
quantum physics affect the interplay between ferromagnetic ordering and
superconductivity in a fundamental way.
