Hitting forbidden induced subgraphs on bounded treewidth graphs

For a fixed graph H, the H-IS-Deletion problem asks, given G, for minimum size of set S?V(G) such that G?S excludes H as an induced subgraph. We are interested in determining, smallest function fH(t) can be solved time fH(t)?nO(1) assuming Exponential Time Hypothesis, where t and n denote treewidth number vertices respectively. show fH(t)=2O(th?2) every on h?3 vertices, fH(t)=2O(t) if is clique or independent set. When deviates slightly from clique, suffers sharp jump: obtained h by removing one edge, then fH(t)=2?(th?2). Moreover, fH(t)=2?(th) when H=Kh,h, answering question Pilipczuk [MFCS 2011].