An FPT Algorithm for Directed Co-Graph Edge Deletion

Abstract

In the directed co-graph edge-deletion problem, we are given a directed graph and an integer k, and the question is whether we can delete, at most, k edges so that the resulting graph is a directed co-graph. In this paper, we make two minor contributions. Firstly, we show that the problem is NP-hard. Then, we show that directed co-graphs are fully characterized by eight forbidden structures, each having, at most, six edges. Based on the symmetry properties and several refined observations, we develop a branching algorithm with a running time of O(2.733k), which is significantly more efficient compared to the brute-force algorithm, which has a running time of O(6k).