Editing to a Graph of Given Degrees

We consider the Editing to a Graph of Given Degrees problem that asks for a graph G, non-negative integers d , k and a function ? : V ( G ) ? { 1 , ? , d } , whether it is possible to obtain a graph G ' from G such that the degree of v is ? ( 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 ? coNP / poly .

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