Editing to a Connected Graph of Given Degrees

  • Petr A. Golovach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8635)

Abstract

The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem that for a given graph G, non-negative integers d,k and a function δ : V(G) → {1,…,d}, asks whether it is possible to obtain a connected graph G′ from G such that the degree of v is δ(v) for any vertex v by at most k edge editing operations. As the problem is NP-complete even if δ(v) = 2, we are interested in the parameterized complexity and show that Edge Editing to a Connected Graph of Given Degrees admits a polynomial kernel when parameterized by d + k. For the special case δ(v) = d, i.e., when the aim is to obtain a connected d-regular graph, the problem is shown to be fixed parameter tractable when parameterized by k only.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Petr A. Golovach
    • 1
    • 2
  1. 1.Department of InformaticsUniversity of BergenNorway
  2. 2.Steklov Institute of Mathematics at St.PetersburgRussian Academy of SciencesRussia

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