Graph Editing to a Given Degree Sequence

Conference paper

DOI: 10.1007/978-3-319-34171-2_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)
Cite this paper as:
Golovach P.A., Mertzios G.B. (2016) Graph Editing to a Given Degree Sequence. In: Kulikov A., Woeginger G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science, vol 9691. Springer, Cham


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 \(\sigma \) by 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 \(2^{O(k(\varDelta +k)^2)}n^2\log n\) for n-vertex graphs, where \(\varDelta =\max \sigma \), i.e., the problem is FPT when parameterized by \(k+\varDelta \). We also show that Editing to a Graph with a Given Degree Sequence has a polynomial kernel when parameterized by \(k+\varDelta \) if only edge additions are allowed, and there is no polynomial kernel unless \(\mathrm{NP}\subseteq \mathrm{coNP}/\text {poly}\) for all other combinations of allowed editing operations.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Steklov Institute of MathematicsRussian Academy of SciencesSt.PetersburgRussia
  3. 3.School of Engineering and Computing SciencesDurham UniversityDurhamUK

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