Complexity and parameterized algorithms for Cograph Editing

Abstract

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. The computational complexity of this problem was open in the past. In this paper, we first show that this problem is NP-hard by a reduction from Exact 3-Cover. Subsequently, we present a parameterized algorithm based on a refined search tree technique with a running time of $O(4.612^k+{\left|V\right|}^{4.5})$, which improves the trivial algorithm of running time $O(6^k+{\left|V\right|}^{4.5})$.