Contagious sets in dense graphs

We also investigate what average degree asserts the existence of small contagious sets. For n≥k≥r, we denote by M(n,k,r) the maximum number of edges in an n-vertex graph G satisfying m(G,r)>k. We determine the precise value of M(n,k,2) and M(n,k,k), assuming that n is sufficiently large compared to k.