  The generating series of the intersection numbers of the stable cohomology
classes on moduli spaces of curves satisfies the string equation and a KdV
hierarchy. Kontsevich's original proof of this result uses a matrix model and
the matrix Airy equation. Witten then recasted Kontsevich's results in terms of
Virasoro algebras, by means of an ingenious mixture of Feynman diagrams
techniques and integrations by parts with some "rather formidable choice" of
the integrands. In this note we show how Witten's formidable choices can be
bartered for standard Feynman diagram manipulations, as soon as one suitably
enlarges the class of Feynman diagrams occurring in the proof.
