Polynomial Kernelization for Removing Induced Claws and Diamonds

  • Marek CyganEmail author
  • 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)


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.


Line Graph Maximal Clique Polynomial Kernel Graph Class Free Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Marek Cygan
    • 1
    Email author
  • 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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