  Cographs are graphs in which no four vertices induce a simple connected path
$P_4$. Cograph editing is to find for a given graph $G = (V,E)$ a set of at
most $k$ edge additions and deletions that transform $G$ into a cograph. This
combinatorial optimization problem is NP-hard. It has, recently found
applications in the context of phylogenetics, hence good heuristics are of
practical importance.
  It is well-known that the cograph editing problem can be solved independently
on the so-called strong prime modules of the modular decomposition of $G$. We
show here that editing the induced $P_4$'s of a given graph is equivalent to
resolving strong prime modules by means of a newly defined merge operation on
the submodules. This observation leads to a new exact algorithm for the cograph
editing problem that can be used as a starting point for the construction of
novel heuristics.
