  The low energy spectrum of a particle in planar honeycomb lattices is
conical, which leads to the unusual electronic properties of graphene. In this
letter we calculate the quasienergy spectra of a charged particle in honeycomb
lattices driven by a strong AC field, which is of fundamental importance for
its time-dependent dynamics. We find that depending on the amplitude, direction
and frequency of external field, many interesting phenomena may occur,
including band collapse, renormalization of velocity of ``light'', gap opening
etc.. Under suitable conditions, with increasing the magnitude of the AC field,
a series of phase transitions from gapless phases to gapped phases appear
alternatively. At the same time, the Dirac points may disappear or change to a
line. We suggest possible realization of the system in Honeycomb optical
lattices.
