A linear kernel for planar feedback vertex set

Authors:
Hans L. Bodlaender;Eelko Penninkx
Affiliations:
Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands
Venue:
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Year:
2008

Citing 26
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Abstract

In this paper we show that Feedback Vertex Set on planargraphs has a kernel of size at most 112k*. We give a polynomialtime algorithm, that given a planar graph G finds a equivalent planargraph G′ with at most 112k* vertices, where k* is the size of the minimumFeedback Vertex Set of G. The kernelization algorithm is basedon a number of reduction rules. The correctness of most of these rulesis shown using a new notion: bases of induced subgraphs. We also showhow to use this new notion to automatically prove safeness of reductionrules and obtain tighter bounds for the size of the kernel.