Parameterized Complexity of Induced H-Matching on Claw-Free Graphs

  • Danny Hermelin
  • Matthias Mnich
  • Erik Jan van Leeuwen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)

Abstract

The Induced H -Matching problem asks to find k disjoint, induced subgraphs isomorphic to H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes amongst others the classical Independent Set and Induced Matching problems. We show that Induced H -Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph of constant size, and even admits a polynomial kernel when H is a clique. Both results rely on a new, strong algorithmic structure theorem for claw-free graphs. To show the fixed-parameter tractability of the problem, we additionally apply the color-coding technique in a nontrivial way. Complementing the above two positive results, we prove the W[1]-hardness of Induced H -Matching for graphs excluding K 1,4 as an induced subgraph. In particular, we show that Independent Set is W[1]-hard on K 1,4-free graphs.

Keywords

Parameterized Complexity Line Graph Decomposition Theorem Polynomial Kernel Graph Class 
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 2012

Authors and Affiliations

  • Danny Hermelin
    • 1
  • Matthias Mnich
    • 2
  • Erik Jan van Leeuwen
    • 3
  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany
  2. 2.Cluster of Excellence “Multimodal Computing and Interaction”Saarland UniversitySaarbrückenGermany
  3. 3.Dept. Computer, Control, Managm. Eng.Sapienza University of RomeItaly

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