  We use low-energy electron microscopy to investigate how graphene is removed
from Ru(0001) and Ir(111) by reaction with oxygen. We find two mechanisms on
Ru(0001). At short times, oxygen reacts with carbon monomers on the surrounding
Ru surface, decreasing their concentration below the equilibrium value. This
undersaturation causes a flux of carbon from graphene to the monomer gas. In
this initial mechanism, graphene is etched at a rate that is given precisely by
the same non-linear dependence on carbon monomer concentration that governs
growth. Thus, during both growth and etching, carbon attaches and detaches to
graphene as clusters of several carbon atoms. At later times, etching
accelerates. We present evidence that this process involves intercalated
oxygen, which destabilizes graphene. On Ir, this mechanism creates observable
holes. It also occurs mostly quickly near wrinkles in the graphene islands,
depends on the orientation of the graphene with respect to the Ir substrate,
and, in contrast to the first mechanism, can increase the density of carbon
monomers. We also observe that both layers of bilayer graphene islands on Ir
etch together, not sequentially.
