  We present the results of million atom electronic quantum transport
calculations for graphene nanoconstrictions with edges that are smooth apart
from atomic scale steps. We find conductances quantized in integer multiples of
2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al.,
Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances
quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic
electron backscattering at the stepped edges that lowers the conductance by one
or more conductance quanta below the adiabatic value. We also show that
conductance plateaus near 0.5*2e2/h can occur as a result of electron
backscattering at stepped edges even in the absence of electron-electron
interactions.
