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
Subject
Computational Mathematics,Computational Theory and Mathematics,Numerical Analysis,Theoretical Computer Science