  We derive the boundary condition for the Dirac equation corresponding to a
tight-binding model on a two-dimensional honeycomb lattice terminated along an
arbitary direction. Zigzag boundary conditions result generically once the
boundary is not parallel to the bonds. Since a honeycomb strip with zigzag
edges is gapless, this implies that confinement by lattice termination does not
in general produce an insulating nanoribbon. We consider the opening of a gap
in a graphene nanoribbon by a staggered potential at the edge and derive the
corresponding boundary condition for the Dirac equation. We analyze the edge
states in a nanoribbon for arbitrary boundary conditions and identify a class
of propagating edge states that complement the known localized edge states at a
zigzag boundary.
