Decomposing color structure into multiplet bases

We illustrate how QCD color structure elegantly can be decomposed into orthogonal multiplet bases corresponding to irreducible representations of SU(N c) with the aid of Wigner 3j and 6j coefficients. We also show how to calculate the relevant 3j and 6j coefficients using multiplet bases and birdtrack techniques and argue that only a relatively small number of Wigner 3j and 6j coefficients are required. For up to six gluons plus quark-antiquark pairs we explicitly calculate all 6j coefficients required for up to NLO calculations.