  The pairing properties of ultracold fermions, with an attractive interaction,
loaded in a honeycomb (graphene-like) optical lattice are studied in a
mean-field approach. We emphasize, in the presence of a harmonic trap, the
unambiguous signatures of the linear dispersion relation of the band structure
around half-filling (i.e. the massless Dirac fermions) in the local order
parameter, in particular in the situations of either imbalance hoping
parameters or imbalance populations. It can also be observed in the system
response to external perturbation, for instance by measuring the pair
destruction rate when modulating the optical lattice depth. Going beyond the
mean-field level, we estimate the critical temperature for the "condensation"
of the preformed pairs.
