Graph Editing to a Given Degree Sequence

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)

Abstract

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.

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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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