Affiliation:
1. School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410083, China
2. Department of Economics, Saarland University, 66123 Saarbrücken, Germany
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).
Funder
National Natural Science Foundation of China
Natural Science Foundation of Hunan Province of China
Postgraduate Scientific Research Innovation Project of Hunan Province