A Polynomial Kernel for Diamond-Free Editing

Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make contain no induced copy of H. We obtain polynomial kernel for this when H is diamond. The incompressibility dichotomy being 3-connected and classical complexity suggest that except complete/empty graph, problems admit kernels only few small graphs Therefore, believe our result an essential step toward complete on compressibility editing. Additionally, give cubic-vertex diamond-free edge deletion problem, which far simpler than previous same size problem.