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  • 标题:Exploiting c-Closure in Kernelization Algorithms for Graph Problems
  • 本地全文:下载
  • 作者:Tomohiro Koana ; Christian Komusiewicz ; Frank Sommer
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2020
  • 卷号:173
  • 页码:65:1-65:17
  • DOI:10.4230/LIPIcs.ESA.2020.65
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number c such that G is c-closed. Fox et al. [SIAM J. Comput. '20] defined c-closure and investigated it in the context of clique enumeration. We show that c-closure can be applied in kernelization algorithms for several classic graph problems. We show that Dominating Set admits a kernel of size k^ð'ª(c), that Induced Matching admits a kernel with ð'ª(c⁷ k⁸) vertices, and that Irredundant Set admits a kernel with ð'ª(c^{5/2} k³) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show.
  • 关键词:Fixed-parameter tractability; kernelization; c-closure; Dominating Set; Induced Matching; Irredundant Set; Ramsey numbers
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