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 6k2 vertex kernels in general graphs. We then prove NP-completeness of s-cycle transversal and (≤s)-cycle transversal in planar graphs for s>3. 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.
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