The 0–1 inverse maximum stable set problem Original Research Article

In this paper we study the 0–1 inverse maximum stable set problem, denoted by image. Given a graph and a fixed stable set, it is to delete the minimum number of vertices to make this stable set maximum in the new graph. We also consider image against a specific algorithm such as image and image, aiming to delete the minimum number of vertices so that the algorithm selects the given stable set in the new graph; we denote them by image and image, respectively. Firstly, we show that they are NP-hard, even if the fixed stable set contains only one vertex. Secondly, we achieve an approximation ratio of image for image. Thirdly, we study the tractability of image for some classes of perfect graphs such as comparability, co-comparability and chordal graphs. Finally, we compare the hardness of image and image for some other classes of graphs.