  Understanding the origin of superconductivity in correlated two-dimensional
materials is a key step in leveraging material engineering techniques for
next-generation nanoscale devices. The recent demonstration of
superconductivity in Bernal bilayer and rhombohedral trilayer graphene, as well
as in a large family of graphene-based moir\'e systems, indicate a common
superconducting mechanism across these platforms. Here we combine first
principles simulations with effective low-energy theories to investigate the
superconducting mechanism and pairing symmetry in rhombohedral stacked graphene
multilayers. We find that a phonon-mediated attraction can quantitatively
explain the main experimental findings, namely the displacement field and
doping dependence of the critical temperature and the presence of two
superconducting regions whose pairing symmetries depend on the parent normal
state. In particular, we find that intra-valley phonon scattering favors a
triplet $f$-wave pairing out of a spin and valley polarized normal state. We
also propose a new and so far unexplored superconducting region at higher hole
doping densities $n_h \approx 4 \times 10^{12}$ cm$^{-2}$, and demonstrate how
this large hole-doped regime can be reached in heterostructures consisting of
monolayer $\alpha$-RuCl$_3$ and rhombohedral trilayer graphene.
