High-order frequency mixing in graphene using a two-color radiation field that consisted of the fundamental and the second harmonic fields of an ultrashort linearly polarized laser pulse is studied. It is shown that the harmonics originated from the interband transitions are efficiently generated in the case of the orthogonally polarized two-color field. In this case, the generated high-harmonics are stronger than those obtained in the parallel polarization case by more than two orders of

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... ude. This is in sharp contrast with the atomic and semiconductor cases, where the parallel polarization case is more preferable. The physical origin of this enhancement is also deduced from the three-step semi-classical electron-hole collision model, extended to graphene with pseudo-relativistic energy dispersion. We also consider the influence of the many particle Coulomb interaction on the HHG process within dynamical Hartree-Fock approximation. Our analysis shows that in all cases we have an overall enhancement of the HHG signal compared with the free-charged carrier model due to the electron-hole attractive interaction.