  We derive color decompositions of arbitrary tree and one-loop QCD amplitudes
into color ordered objects called primitive amplitudes. Furthermore, we derive
general fermion flip and reversion identities spanning the null space among the
primitive amplitudes and use them to prove that all color ordered tree
amplitudes of massless QCD can be written as linear combinations of color
ordered tree amplitudes of $\mathcal{N}=4$ super Yang-Mills theory.
