Incompressibility of H-free edge modification problems: Towards a dichotomy

Given a graph G and an integer k, the H-free Edge Editing problem is to find whether there exist at most k pairs of vertices in such that changing adjacency results without any induced copy H. Nontrivial polynomial kernels are known for some graphs H with 4 vertices, but starting from 5 only if either complete or empty. This suggests conjecture no other least where admits kernel. Towards this goal, we obtain set nine 5-vertex every H?H, incompressible complexity assumption NP?coNP/poly holds, then five neither nor We similar also Deletion/Completion.