Parameterized complexity of induced graph matching on claw-free graphs

Danny Hermelin, Matthias Mnich, Erik Jan Van Leeuwen

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11 Scopus citations

Abstract

The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced Graph Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph, and even admits a polynomial kernel when H is a complete graph. Both results rely on a new, strong, and generic algorithmic structure theorem for claw-free graphs. Complementing the above positive results, we prove W[1] -hardness of Induced Graph Matching on graphs excluding K1,4 as an induced subgraph, for any fixed complete graph H. In particular, we show that Independent Set is W[1] -hard on K1,4-free graphs. Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs. We show that the problem is either polynomial-time solvable or NP-complete, depending on the connectivity of H and the structure of G.

Original languageEnglish
Pages (from-to)513-560
Number of pages48
JournalAlgorithmica
Volume70
Issue number3
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Algorithms and data structures
  • Claw-free graphs
  • Fixed-parameter tractability
  • Induced matchings

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