  Anderson's orthogonality catastrophe in graphene, at energies close to the
Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality
catastrophe is suppressed, due to the vanishing density of states at the Dirac
point. In the presence of preexisting localized states at the Dirac energy, the
orthogonality catastrophe shows similar features to those found in normal
metals with a finite density of states at the Fermi level. The implications for
the Kondo effect induced by magnetic impurities, and for the Fermi edge
singularities in tunneling processes are also discussed.
