We present predictions of reaction rate constants for dissociative adsorption reactions of COx (x = 1, 2) and NOx (x = 1, 2) molecules on the basal graphite (0001) surface based on potential energy surfaces (PES) obtained by the integrated ONIOM(B3LYP: DFTB-D) quantum chemical hybrid approach with dispersion-augmented density functional tight binding(DFTB-D) as low level method. Following an a priori methodology developed in a previous investigation of water dissociative adsorption reactions on graphite, we used a C94H24 dicircumcoronene graphene slab as model system for the graphite surface in finite-size molecular structure investigations, and single adsorbate molecules reacting with the pristine graphene sheet. By employing the ONIOM PES information in RRKM theory we predict reaction rate constants in the temperature range between 1000 and 5000 K. We find that among COx and NOx adsorbate species, the dissociative adsorption reactions of CO2 and both radical species NO and NO2 are likely candidates as a cause for high temperature oxidation and erosion of graphite (0001) surfaces, whereas reaction with CO is not likely to lead to long-lived surface defects. High temperature quantum chemical molecular dynamics simulations (QM/MD) at T = 5000 K using on-the-fly DFTB-D energies and gradients confirm the results of our PES study.