  We study the formation of Majorana fermions in honeycomb-lattice structures
in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the
proximity of an s-wave superconductor. We show that an exact mapping exists
between an anisotropic hexagonal-lattice nanoribbon at k = 0 and a
one-dimensional chain, for which the existence of Majorana fermions has been
extensively discussed. Consequently we can predict the conditions for the
emergence of Majorana fermions at the edges of such ribbon, and relate the
existence of Majoranas to a band inversion in the bulk band structure. Moreover
we find that similar situations arise in isotropic lattices and we give some
examples which show the formation of Majorana fermions in these structures.
