  Motivated by recent discovery of correlated insulating and superconducting
behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice
doped close to the van Hove singularity, using the truncated unity functional
renormalization group approach. We consider an extended Hubbard model on the
honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions,
and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By
varying the strength of the nearest-neighbor exchange coupling and Coulomb
repulsion as free parameters, we present rich ground-state phase diagrams which
contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave
superconducting phases, the commensurate and incommensurate spin- and
charge-density-wave phases, and the ferromagnetic phase. In the absence of the
exchange coupling and for small value of the nearest-neighbor repulsion, the
four-sublattice spin-density-wave phase is generated right around the van Hove
filling, while the chiral $d$-wave superconductivity emerges slightly away from
it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed
by weak nearest-neighbor exchange coupling in our calculations. We argue that
this suppression might be one of the reasons why the chiral superconductivity
proposed for doped graphene has not yet been observed experimentally.
