Editing to a Planar Graph of Given Degrees

  • Konrad K. Dabrowski
  • Petr A. Golovach
  • Pim van ’t Hof
  • Daniël Paulusma
  • Dimitrios M. Thilikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9139)

Abstract

We consider the following graph modification problem. Let the input consist of a graph \(G=(V,E)\), a weight function \(w:V\cup E\rightarrow \mathbb {N}\), a cost function \(c:V\cup E\rightarrow \mathbb {N}\) and a degree function \(\delta :V\rightarrow \mathbb {N}_0\), together with three integers \(k_v\), \(k_e\) and C. The question is whether we can delete a set of vertices of total weight at most \(k_v\) and a set of edges of total weight at most \(k_e\) so that the total cost of the deleted elements is at most C and every non-deleted vertex v has degree \(\delta (v)\) in the resulting graph \(G'\). We also consider the variant in which \(G'\) must be connected. Both problems are known to be \(\mathsf{NP}\)-complete and \(\mathsf{W}[1]\)-hard when parameterized by \(k_v+k_e\). We prove that, when restricted to planar graphs, they stay \(\mathsf{NP}\)-complete but have polynomial kernels when parameterized by \(k_v+k_e\).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Konrad K. Dabrowski
    • 1
  • Petr A. Golovach
    • 2
  • Pim van ’t Hof
    • 3
  • Daniël Paulusma
    • 1
  • Dimitrios M. Thilikos
    • 4
  1. 1.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  2. 2.Department of InformaticsUniversity of BergenBergenNorway
  3. 3.School of Built EnvironmentRotterdam University of Applied SciencesRotterdamThe Netherlands
  4. 4.Department of Mathematics, Computer Technology Institute and Press “Diophantus”, Patras, GreeceNational and Kapodistrian University of Athens, Athens, Greece and AlGCo Project-team, CNRS, LIRMMMontpellierFrance

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