  We study the integer and fractional quantum Hall effect on a honeycomb
lattice at half-filling (graphene) in the presence of disorder and
electron-electron interactions. We show that the interactions between the
delocalized chiral edge states (generated by the magnetic field) and
Anderson-localized surface states (created by the presence of zig-zag edges)
lead to edge reconstruction. As a consequence, the point contact tunneling on a
graphene edge has a non-universal tunneling exponent, and the Hall conductivity
is not perfectly quantized in units of $e^2/h$. We argue that the
magneto-transport properties of graphene depend strongly on the strength of
electron-electron interactions, the amount of disorder, and the details of the
edges.
