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On the Induced Matching Problem Kanj, Iyad A. Pelsmajer, Michael J. Xia, Ge Schaefer, Marcus Induced matching bounded genus graphs parameterized algorithms kernel We study extremal questions on induced matchings in several natural graph classes. We argue that these questions should be asked for twinless graphs, that is graphs not containing two vertices with the same neighborhood. We show that planar twinless graphs always contain an induced matching of size at least $n/40$ while there are planar twinless graphs that do not contain an induced matching of size $(n+10)/27$. We derive similar results for outerplanar graphs and graphs of bounded genus. These extremal results can be applied to the area of parameterized computation. For example, we show that the induced matching problem on planar graphs has a kernel of size at most $40k$ that is computable in linear time; this significantly improves the results of Moser and Sikdar (2007). We also show that we can decide in time $O(91^k + n)$ whether a planar graph contains an induced matching of size at least $k$. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Iyad A. Kanj and Michael J. Pelsmajer and Ge Xia and Marcus Schaefer 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1361 urn:nbn:de:0030-drops-13618 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1361 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode