A 9k kernel for nonseparating independent set in planar graphs

Authors:
Łukasz Kowalik;Marcin Mucha
Affiliations:
Institute of Informatics, University of Warsaw, Poland;Institute of Informatics, University of Warsaw, Poland
Venue:
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2012

Citing 7
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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).