  Due to its fourfold spin-valley degeneracy, graphene in a strong magnetic
field may be viewed as a four-component quantum Hall system. We investigate the
consequences of this particular structure on a possible, yet unobserved,
fractional quantum Hall effect in graphene within a trial-wavefunction approach
and exact-diagonalisation calculations. This trial-wavefunction approach
generalises an original idea by Halperin to account for the SU(2) spin in
semiconductor heterostructures with a relatively weak Zeeman effect. Whereas
the four-component structure at a filling factor nu=1/3 adds simply a
SU(4)-ferromagnetic spinor ordering to the otherwise unaltered Laughlin state,
the system favours a valley-unpolarised state at nu=2/5 and a completely
unpolarised state at nu=4/9. Due to the similar behaviour of the interaction
potential in the zero-energy graphene Landau level and the first excited one,
we expect these states to be present in both levels.
