Abstract
We study kernelization (a kind of efficient preprocessing) for NP-hard problems on planar graphs. Our main result is a kernel of size at most 9k vertices for the Planar Maximum Nonseparating Independent Set problem. A direct consequence of this result is that Planar Connected Vertex Cover has no kernel with at most 9/8k vertices, assuming P ≠ NP. We also show a very simple 5k-vertices kernel for Planar Max Leaf, which results in a lower bound of 5/4k vertices for the kernel of Planar Connected Dominating Set (also under P ≠ NP).
Work supported by the National Science Centre (grant N N206 567140).
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Kowalik, Ł., Mucha, M. (2012). A 9k Kernel for Nonseparating Independent Set in Planar Graphs. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_18
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DOI: https://doi.org/10.1007/978-3-642-34611-8_18
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