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We perform a general group-theoretical study of the Kondo problem inmonolayer and bilayer graphene around the charge neutrality point. Utilizingthe group representation theory, we derive from symmetry considerations afamily of the Kondo models for all symmetric placements with either 3- or6-fold rotational axis of an impurity atom in an arbitrary orbital state. Wefind six possible classes of the partially anisotropic four-channel Kondomodel. As the key result, we argue several possibilities to realize the regimeof the dominant channel-symmetric two-channel Kondo effect, protected by thelocal symmetry and specifics of the graphene band structure. Our findings openprospects for the observation of the rich multi-channel Kondo physics ingraphene and the associated non-Fermi-liquid behavior.

Kondo effect in monolayer and bilayer graphene: physical realizations of the multi-channel Kondo models