  Proposals for superconductivity emerging from correlated electrons in the
doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet
to $p+ip$ triplet pairing, depending on the considered range of doping and
interaction strength, as well as the approach used to analyze the pairing
instabilities. Here, we consider these scenarios using large-scale dynamic
cluster approximation (DCA) calculations to examine the evolution in the
leading pairing symmetry from weak to intermediate coupling strength. These
calculations focus on doping levels around the van Hove singularity (VHS) and
are performed using DCA simulations with an interaction-expansion
continuous-time quantum Monte Carlo cluster solver. We calculated explicitly
the temperature dependence of different uniform superconducting pairing
susceptibilities and found a consistent picture emerging upon gradually
increasing the cluster size: while at weak coupling the $d+id$ singlet pairing
dominates close to the VHS filling, an enhanced tendency towards $p$-wave
triplet pairing upon further increasing the interaction strength is observed.
The relevance of these systematic results for existing proposals and ongoing
pursuits of odd-parity topological superconductivity are also discussed.
