  It has been proposed that interactions lead to ferromagnetism on a zigzag
edge of a graphene sheet. While not yet directly studied experimentally,
dramatically improving techniques for making and studying clean zigzag edges
may soon make this possible. So far, most theoretical investigations of this
claim have been based on mean field theories or more exact calculations using
the Hubbard model. But long-range Coulomb interactions are unscreened in
graphene so it is important to consider their effects. We study rather general
non-local interactions, including of Coulomb $1/r$ form, using the technique of
projection to a strongly interacting edge Hamiltonian, valid at first order in
the interactions. The ground states as well as electron/hole and exciton
excitations are studied in this model. Our results indicate that ferromagnetism
survives with unscreened Coulomb interactions.
