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Polynomial Kernelization for Removing Induced Claws and Diamonds

  • Marek Cygan
  • Marcin Pilipczuk
  • Michał Pilipczuk
  • Erik Jan van Leeuwen
  • Marcin Wrochna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

A graph is called {claw, diamond}-free if it contains neither a claw (a \(K_{1,3}\)) nor a diamond (a \(K_4\) with an edge removed) as an induced subgraph, or, equivalently, it is a line graph of a triangle-free graph. We consider the parameterized complexity of the {claw, diamond}-free Edge Deletion problem, where given a graph G and a parameter k, the question is whether one can remove at most k edges from G to obtain a {claw, diamond}-free graph. Our main result is that this problem admits a polynomial kernel. We also show that, even on instances with maximum degree 6, the problem is NP-complete and cannot be solved in time \(2^{o(k)}\cdot |V(G)|^{\mathcal {O}(1)}\), assuming the Exponential Time Hypothesis.

Keywords

Line Graph Maximal Clique Polynomial Kernel Graph Class Free Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Marek Cygan
    • 1
  • Marcin Pilipczuk
    • 2
  • Michał Pilipczuk
    • 1
  • Erik Jan van Leeuwen
    • 3
  • Marcin Wrochna
    • 1
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland
  2. 2.Department of Computer ScienceUniversity of WarwickWarwickUK
  3. 3.Max-Planck Institut Für InformatikSaarbrückenGermany

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