For any integer d, the Kontsevich graph complex GC^2_d and the oriented graph complex OGC^2_{d+1} are connected by a zigzag of quasi-isomorphisms of dg Lie algebras.
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The oriented graph complex revisited
For any integer d, the Kontsevich graph complex GC^2_d and the oriented graph complex OGC^2_{d+1} are connected by a zigzag of quasi-isomorphisms of dg Lie algebras.