Existence and topological stability of Fermi points in multilayered graphene

We study the existence and topological stability of Fermi points in a graphene layer and stacks with many layers. We show that the discrete symmetries (spacetime inversion) stabilize the Fermi points in monolayer, bilayer and multilayer graphene with orthorhombic stacking. The bands near $k=0$ and $\epsilon=0$ in multilayers with the Bernal stacking depend on the parity of the number of layers, and Fermi points are unstable when the number of layers is odd. The low energy changes in the electronic structure induced by commensurate perturbations which mix the two Dirac points are also investigated.