Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover Original Research Article

Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class image, where for each graph G in image, the removal of a set of at most k vertices from G results in a graph in the base graph class image. (If image is the class of edgeless graphs, image is the class of graphs with bounded vertex cover.)