### 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.

Original language | English |
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Title of host publication | Algorithms - ESA 2012 |

Subtitle of host publication | 20th Annual European Symposium Ljubljana, Slovenia, September 2012 Proceedings |

Editors | Leah Epstein, Paolo Ferragina |

Publisher | Springer |

Pages | 624-635 |

ISBN (Electronic) | 978-3-642-33090-2 |

ISBN (Print) | 978-3-642-33089-6 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 7501 |

## Cite this

Hermelin, D., Mnich, M., & van Leeuwen, E. J. (2012). Parameterized Complexity of Induced H-Matching on Claw-Free Graphs. In L. Epstein, & P. Ferragina (Eds.),

*Algorithms - ESA 2012: 20th Annual European Symposium Ljubljana, Slovenia, September 2012 Proceedings*(pp. 624-635). Springer. Lecture Notes in Computer Science, Vol.. 7501 https://doi.org/10.1007/978-3-642-33090-2_54