Multistage Vertex Cover

Abstract The NP-complete Vertex Cover problem asks to cover all edges of a graph by small (given) number vertices. It is among the most prominent graph-algorithmic problems. Following recent trend in studying temporal graphs (a sequence graphs, so-called layers, over same vertex set but, time, changing edge sets), we initiate study Multistage . Herein, given graph, goal find for each layer and guarantee that two sets every consecutive layers differ not too much (specified parameter). We show that, different from classic some other dynamic or variants it, computationally hard even fairly restricted settings. On positive side, however, also spot several fixed-parameter tractability results based on themost natural parameterizations.