“…Besides cliques and empty graphs, it is known for certain graphs H of at most 4 vertices (diamond [5,9], path [6,15,16], paw [7,13], and their complements) that H-free Edge Editing has a polynomial kernel, but these algorithms use very specific arguments exploiting the structure of H-free graphs. As there is a very deep known structure theory of claw-free (i.e, K 1,3 -free) graphs, it might be possible to obtain a polynomial kernel for Claw-free Edge Editing, but this is currently a major open question [4,10,12]. However, besides cliques and empty graphs, no H with at least 5 vertices is known where H-free Edge Editing has a polynomial kernel and there is no obvious candidate H for which one would expect a kernel.…”