Graph cohomology classes in the Batalin-Vilkovisky formalism

We give a conceptual formulation of Kontsevich's `dual construction' producing graph cohomology classes from a differential graded Frobenius algebra with an odd scalar product. Our construction -- whilst equivalent to the original one -- is combinatorics-free and is based on the Batalin-Vilkovisky formalism, from which its gauge-independence is immediate.