  We present a rigorous and rather self-contained analysis of the Verdet
constant in graphene- like materials. We apply the gauge-invariant magnetic
perturbation theory to a nearest- neighbour tight-binding model and obtain a
relatively simple and exactly computable formula for the Verdet constant, at
all temperatures and all frequencies of sufficiently large absolute value.
Moreover, for the standard nearest neighbour tight-binding model of graphene we
show that the transverse component of the conductivity tensor has an asymptotic
Taylor expansion in the external magnetic field where all the coefficients of
even powers are zero.
