Vacancy induced localized states in graphene*

We show, analytically, that vacancies in an half-filled honeycomb lattice induce the formation of quasi-localized electronic states. If particle-hole symmetry is broken, these states become resonances close to the Fermi level. We also calculate numerically the electronic density of states for a finite density of vacancies, and discuss the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductor.