Editing to a Graph of Given Degrees

We consider the Editing to a Graph of Given Degrees problem that for a graph G, non-negative integers d, k and a function delta : V (G) -> {1,..., d}, asks whether it is possible to obtain a graph G' from G such that the degree of v is delta(v) for any vertex v by at most k vertex or edge deletions or edge additions. We construct an FPT-algorithm for EDITING TO A GRAPH OF GIVEN DEGREES parameterized by d + k. We complement this result by showing that the problem has no polynomial kernel unless NP subset of coNP/poly.