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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 atmost $k$ edge additions and deletions that transform $G$ into a cograph. Thiscombinatorial optimization problem is NP-hard. It has, recently foundapplications in the context of phylogenetics, hence good heuristics are ofpractical importance.  It is well-known that the cograph editing problem can be solved independentlyon the so-called strong prime modules of the modular decomposition of $G$. Weshow here that editing the induced $P_4$'s of a given graph is equivalent toresolving strong prime modules by means of a newly defined merge operation onthe submodules. This observation leads to a new exact algorithm for the cographediting problem that can be used as a starting point for the construction ofnovel heuristics.

Techniques for the Cograph Editing Problem: Module Merge is equivalent to Editing P4s