  Motivated by the observation of even denominator fractional quantum Hall
effect in the $n=3$ Landau level of monolayer graphene [Y. Kim $\textit{et
al.}$, Nature Physics $\textbf{15}$, 154 (2019)], we consider a
Bardeen-Cooper-Schrieffer variational state for composite fermions and find
that the composite-fermion Fermi sea in this Landau level is unstable to an
$f$-wave pairing. Analogous calculation suggests the possibility of a $p$-wave
pairing of composite fermions at half filling in the $n=2$ graphene Landau
level, whereas no pairing instability is found at half filling in the $n=0$ and
$1$ graphene Landau levels. The relevance of these results to experiments is
discussed.
