  We review an approach for the computation of Feynman integrals by use of
multiple polylogarithms, with an emphasis on the related criterion of linear
reducibility of the graph. We show that the set of graphs which satisfies the
linear reducibility with respect to both Symanzik polynomials is closed under
taking minors. As a step towards a classification of Feynman integrals, we
discuss the concept of critical minors and exhibit an example at three loops
with four on-shell legs.
