  The weak intrinsic spin-orbit coupling in graphene can be greatly enhanced by
proximity coupling. Here we report on the proximity-induced spin-orbit coupling
in graphene transferred by hexagonal boron nitride (hBN) onto the topological
insulator Bi$_{1.5}$Sb$_{0.5}$Te$_{1.7}$Se$_{1.3}$ (BSTS) which was grown on a
hBN substrate by vapor solid synthesis. Phase coherent transport measurements,
revealing weak localization, allow us to extract the carrier density-dependent
phase coherence length $l_\phi$. While $l_\phi$ increases with increasing
carrier density in the hBN/graphene/hBN reference sample, it decreases in
BSTS/graphene due to the proximity-coupling of BSTS to graphene. The latter
behavior results from D'yakonov-Perel-type spin scattering in graphene with a
large proximity-induced spin-orbit coupling strength of at least 2.5 meV.
