  We review quantization of gauge fields using algebraic properties of
3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian
gauge theory quantized in a covariant gauge from scalar integrands for
connected 3-regular graphs, obtained from the two Symanzik polynomials. The
transition to the full gauge theory amplitude is obtained by the use of a
third, new, graph polynomial, the corolla polynomial. This implies effectively
a covariant quantization without ghosts, where all the relevant signs of the
ghost sector are incorporated in a double complex furnished by the corolla
polynomial -we call it cycle homology- and by graph homology.
