  Theoretical studies of the fractional quantum Hall effect (FQHE) in graphene
have so far focused on the plausibility and stability of the previously known
FQHE states for the interaction matrix elements appropriate for graphene. We
consider FQHE for SU(4) symmetry, as appropriate for the situation when all
four spin and valley Landau bands are degenerate, and predict new FQHE states
that have no analog in GaAs. These result from an essential interplay between
the two-fold spin and valley degeneracies at fractions of the form
$\nu=n/(2pn\pm 1)$, for $n\geq 3$. Conditions are outlined for the observation
of these states and quantum phase transitions between them; the structure of
these states and their excitations is also described.
