Exploiting $c$-Closure in Kernelization Algorithms for Graph Problems
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Publication:5048305
DOI10.1137/21M1449476zbMATH Open1503.05118arXiv2005.03986MaRDI QIDQ5048305
Author name not available (Why is that?)
Publication date: 15 November 2022
Published in: (Search for Journal in Brave)
Abstract: 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 such that G is c-closed. Fox et al. [ICALP '18] 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^O(c), that Induced Matching admits a kernel with O(c^7*k^8) vertices, and that Irredundant Set admits a kernel with O(c^(5/2)*k^3) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show.
Full work available at URL: https://arxiv.org/abs/2005.03986
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