  One of the many remarkable properties of graphene is that in the low energy
limit the dynamics of its electrons can be effectively described by the
massless Dirac equation. This has prompted investigations of graphene based on
the lattice simulation of a system of 2-dimensional fermions on a square
staggered lattice. We demonstrate here how to construct the path integral for
graphene working directly on the graphene hexagonal lattice. For the nearest
neighbor tight binding model interacting with a long range Coulomb interaction
between the electrons, this leads to the hybrid Monte Carlo algorithm with no
sign problem. The only approximation is the discretization of the Euclidean
time. So as we extrapolate to the time continuum limit, the exact tight binding
solution maybe found numerically to arbitrary precession on a finite hexagonal
lattice. The potential for this approach is tested on a single hexagonal cell.
