A universal formula for deformation quantization on Kähler manifolds

•We give an explicit local formula for any star product with separation of variables.•Terms of the formula are parametrized by acyclic directed graphs.•The formula is proved by elementary combinatorial considerations.

We give an explicit local formula for any formal deformation quantization, with separation of variables, on a Kähler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.