Wheel-free deletion is W[2]-hard

Abstract

We show that the two problems of deciding whether k vertices or k edges can be deleted from a graph to obtain a wheel-free graph is W[2]-hard. This immediately implies that deciding whether k edges can be added to obtain a graph that contains no complement of a wheel as an induced subgraph is W[2]-hard, thereby resolving an open problem of Heggernes et al. [7] (STOC07) who ask whether there is a polynomial time recognizable hereditary graph class Π with the property that computing the minimum Π-completion is W[t]-hard for some t. © 2008 Springer-Verlag Berlin Heidelberg.