  Within the Hartree Fock- RPA analysis, we derive the spin wave spectrum for
the weak ferromagnetic phase of the Hubbard model on the honeycomb lattice.
Assuming a uniform magnetization, the polar (optical) and acoustic branches of
the spin wave excitations are determined. The bipartite lattice geometry
produces a q-dependent phase difference between the spin wave amplitudes on the
two sub-lattices. We also find an instability of the uniform weakly magnetized
configuration to a weak antiferromagnetic spiraling spin structure, in the
lattice plane, with wave vector Q along the Gamma-K direction, for electron
densities n>0.6. We discuss the effect of diagonal disorder on both the
creation of electron bound states, enhancement of the density of states, and
the possible relevance of these effects to disorder induced ferromagnetism, as
observed in proton irradiated graphite.
