The calculation of the local density of electronic states of graphene with vacancies, using the method of Jacobi matrix, was performed. It was shown that for atoms in the sublattice with a vacancy the local density of electronic states conserves the Dirac singularity, similarly as in an ideal graphene. A quasi-Dirac singularity was observed also in the phonon spectra of graphite for the atom displacements in the direction perpendicular to layers. Changes of phonon spectra of graphite intercalated with various metals were analyzed. On the basis of our results and using the BCS theory and Eliashberg equation we proposed what dynamic properties an intercalated graphite system should show to obtain an increased Tc.