  Motivated by the recent experimental detection of superconductivity in Bernal
bilayer (AB) and rhombohedral trilayer (ABC) graphene, we study the emergence
of superconductivity in multilayer graphene based on a Kohn-Luttinger (KL)-like
mechanism in which the pairing glue is the screened Coulomb interaction. We
find that electronic interactions alone can drive superconductivity in AB
bilayer graphene and ABC trilayer graphene with the critical temperatures in
good agreement with the experimentally observed ones, allowing us to further
predict superconductivity from electronic interactions in Bernal ABA trilayer
and ABAB tetralayer and rhombohedral ABCA tetralayer graphene. By comparing the
critical temperatures ($T_c$) of these five non-twisted graphene stacks, we
find that the ABC trilayer graphene possesses the highest $T_c\sim100$ mK.
After considering the enhancement of superconductivity due to Ising spin-orbit
coupling, we observe that the AB bilayer graphene has the largest enhancement
in the critical temperature, increasing from 23 mK to 143 mK. The
superconducting behaviors in these non-twisted graphene stacks could be
explained by the order parameters (OPs). The OPs of Bernal stacks preserve
intravalley $C_3$ symmetry, whereas rhombohedral stacks break it. In all
stacks, the OPs have zeroes and change signs between valleys, which means that
these multilayers of graphene are nodal spin-triplet superconductors. Moreover,
dressing the purely electronic interaction with acoustic phonons, we observe
minor changes of the critical temperatures in these five stacks. We adopt the
KL-like mechanism to investigate the tendency of superconductivity in
multilayer graphene without fitting parameters, which could provide guidance to
future experiments exploring superconductivity in non-twisted graphene.
