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.
Supported by ERC StG project PAAl no. 259515. A full version of this paper can be found on the arXiv.
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Hermelin, D., Mnich, M., van Leeuwen, E.J. (2012). Parameterized Complexity of Induced H-Matching on Claw-Free Graphs. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_54
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DOI: https://doi.org/10.1007/978-3-642-33090-2_54
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