Wheel-Free Deletion Is W[2]-Hard

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 isW [2]-hard, thereby resolving an open problem of Heggernes et. al. [7] (STOC07) who asks whether there is a polynomial time recognizible hereditary graph class Π with the property that computing the minimum Π-completion is W [t]-hard for some t.