On the independent set interdiction problem

Abstract

The purpose of the independent set interdiction problem in the weighted graph $G$ is to determine a set of vertices $R^*$ such that the weight of the maximum independent set in $G-R^*$ is minimized. We define an approximate solution for this problem. Then, an upper bound for the relative error of this problem is obtained. We show that the limit of the relative error of the independent set interdiction problem in some subclasses of the generalized Petersen graphs is zero as the number of vertices tends to infinity.