On the Complexity of the Maximum Independent Set Reconfiguration Problem

Abstract

We study the complexity of the polynomially equivalent Minimum Vertex Cover Reconfiguration and Maximum Independent Set Reconfiguration problems on a variety of graph classes, which ask whether there exists a reconfiguration sequence between two minimum vertex covers/maximum independent sets S and T of a graph G. The problems are studied under the token jumping and token sliding models, which turn out to be equivalent in this context. We show that the problems are in P when restricted to bipartite graphs, PSPACE-complete when restricted to planar graphs, as well as a list of results on a variety of other graph classes.