  In graphene, the approximate SU(4) symmetry associated with the spin and
valley degrees of freedom in the quantum Hall (QH) regime is reflected in the
4-fold degeneracy of graphene's Landau levels (LL's). Interactions and the
Zeeman effect break such approximate symmetry and lift the corresponding
degeneracy of the LLs. We study how the breaking of the approximate SU(4)
symmetry affects the properties of graphene's QH edge modes located in
proximity to a superconductor. We show how the lifting of the 4-fold degeneracy
qualitatively modifies the transport properties of the QH-superconductor
heterojunction. For the zero LL, by placing the edge modes in proximity to a
superconductor, it is in principle possible to realize a 1D topological
superconductor supporting Majoranas in the presence of sufficiently strong
Zeeman field. We estimate the topological gap of such a topological
superconductor and relate it to the properties of the QH-superconductor
interface.
