We report on the characterization of the electrical breakdown (EB) process for the formation of tunneling nanogaps in single-layer graphene. In particular, we investigated the role of oxygen in the breakdown process by varying the environmental conditions (vacuum and ambient conditions). We show that the density of oxygen molecules in the chamber is a crucial parameter that defines the physical breakdown process: at low density, the graphene lattice is sublimating, whereas at high density, the process involved is oxidation, independent of the substrate material. To estimate the activation energies of the two processes, we use a scheme which consists of applying voltage pulses across the junction during the breakdown. By systematically varying the voltage pulse length, and estimating the junction temperature from a 1D thermal model, we extract activation energies which are consistent with the sublimation of graphene under high vacuum and the electroburning process under air. Our study demonstrates that, in our system, a better control of the gap formation is achieved in the sublimation regime.