  We introduce a white graph expansion for the method of perturbative
continuous unitary transformations when implemented as a linked cluster
expansion. The essential idea behind an expansion in white graphs is to perform
an optimized bookkeeping during the calculation by exploiting the
model-independent effective Hamiltonian in second quantization and the
associated inherent cluster additivity. This appoach is shown to be especially
well suited for microscopic models with many coupling constants, since the
total number of relevant graphs is drastically reduced. The white graph
expansion is exemplified for a two-dimensional quantum spin model of coupled
two-leg XXZ ladders.
