  Motivated by the problem of deformation quantization we introduce and study
directed graph complexes with oriented loops and wheels. We develop some
technique for computing cohomology of such graph complexes and apply it to
several concrete examples such as wheeled completion of the operad of strongly
homotopy Lie algebras and the wheeled completion of the dg prop of Poisson
structures. We prove also a deformation quantization theorem of wheeled Poisson
structures on arbitrary formal graded manifolds.
