  We develop a theory for interlayer pairing of chiral electrons in graphene
materials which results in an unconventional superconducting (S) state with
s-wave spin-triplet order parameter. In a pure bilayer graphene, this
superconductivity exhibits a gapless property with an exotic effect of
temperature-induced condensation causing an increase of the pairing amplitude
(PA) with increasing temperature. We find that a finite doping opens a gap in
the excitation spectrum and weakens this anomalous temperature-dependence. We
further explore the possibility of realizing variety of pairing patterns with
different topologies of the Fermi surface, by tuning the difference in the
doping of the two layers. In trillayer graphene, the interlayer
superconductivity is characterized by a two components order parameter which
can be used to define two distinct phases in which only one of the components
is non vanishing. For ABA stacking the stable state is determined by a
competition between these two phases. By varying the relative amplitude of the
corresponding coupling strenghes, a first order phase transition can occur
between these two phases. For ABC stacking, we find that the two phases coexist
with a possibility of a similar phase transition which turns out to be second
order.
