  We discuss how to construct tight-binding models for ultra cold atoms in
honeycomb potentials, by means of the maximally localized Wannier functions
(MLWFs) for composite bands introduced by Marzari and Vanderbilt [1]. In
particular, we work out the model with up to third-nearest neighbors, and
provide explicit calculations of the MLWFs and of the tunneling coefficients
for the graphene-lyke potential with two degenerate minima per unit cell.
Finally, we discuss the degree of accuracy in reproducing the exact Bloch
spectrum of different tight-binding approximations, in a range of typical
experimental parameters.
