Comment on: Decomposition of structural learning about directed acyclic
  graphs [1]
  We propose an alternative proof concerning necessary and sufficient
conditions to split the problem of searching for d-separators and building the
skeleton of a DAG into small problems for every node of a separation tree T.
The proof is simpler than the original [1]. The same proof structure has been
used in [2] for learning the structure of multivariate regression chain graphs
(MVR CGs).
