  We analyze interaction effects on boundary states of single layer graphene.
Near a half filled band, both short and long-ranged interactions lead to a
fully spin polarized configuration. In addition, the band of boundary states
acquires a finite dispersion as function of the momentum parallel to the edge,
induced by the interactions. Away from half filling the wavefunction develops
charge correlations similar to those in a Wigner crystal, and the spin strongly
alternates with the occupation of the boundary states. For certain fillings the
ground state has a finite linear momentum, leading to the formation of
persistent currents.
