Kernelization for cycle transversal problems

Authors:
Ge Xia;Yong Zhang
Affiliations:
Department of Computer Science, Lafayette College, Easton, PA 18042, USA;Department of Computer Science, Kutztown University, Kutztown, PA 19530, USA
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

We present new kernelization results for two problems, s-cycle transversal and (@?s)-cycle transversal, when s is 4 or 5. We show that 4-cycle transversal and @?4-cycle transversal admit 6k^2 vertex kernels in general graphs. We then prove NP-completeness of s-cycle transversal and (@?s)-cycle transversal in planar graphs for s3. We show the following linear vertex kernels in planar graphs-a 74k vertex kernel for 4-cycle transversal; a 32k vertex kernel for (@?4)-cycle transversal; a 266k vertex kernel for (@?5)-cycle transversal.