文章基本信息

标题：On the Induced Matching Problem
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作者：Iyad A. Kanj ; Michael J. Pelsmajer ; Ge Xia 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2008
卷号：1
页码：397-408
DOI：10.4230/LIPIcs.STACS.2008.1361
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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 $k$.
关键词：Induced matching; bounded genus graphs; parameterized algorithms; kernel