  The core of the vortex in a general superconducting order parameter in
graphene is argued to be ordered, with the possible order parameters forming
the algebra U(1) X Cl(3), where Cl(3) is the three dimensional Clifford
algebra. A sufficiently strong Zeeman coupling of the magnetic field of the
vortex to the electron spin breaks the degeneracy in the core in favor of the
anomalous quantum Hall state. I consider a variety of superconducting
condensates on the honeycomb lattice and demonstrate the surprising
universality of this result. A way to experimentally determine the outcome of
the possible competition between different types of orders in the core is
proposed.
