Graph Editing to a Given Degree Sequence

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We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence σby at most k vertex or edge deletions and edge additions. We show that the problem is W[1]-hard when parameterized by k for any combination of the allowed editing operations. From the positive side, we show that the problem can be solved in time 2ᵒ⁽ᵏ⁽Δ⁺ᵏ⁾²⁾n² log n for n-vertex graphs, where Δ=max σ, i.e., the problem is FPT when parameterized by k+Δ. We also show that Editing to a Graph with a Given Degree Sequence has a polynomial kernel when parameterized by k+Δif only edge additions are allowed, and there is no polynomial kernel unless NP coNP/poly for all other combinations of allowed editing operations.