On the small cycle transversal of planar graphs

@article{Xia2011OnTS,
  title={On the small cycle transversal of planar graphs},
  author={Ge Xia and Yong Zhang},
  journal={Theor. Comput. Sci.},
  year={2011},
  volume={412},
  pages={3501-3509}
}
We consider the problem of finding a k-edge transversal set that intersects all (simple) cycles of length at most s in a planar graph, where s>=3 is a constant. This problem, referred to as Small Cycle Transversal, is known to be NP-complete. We present a polynomial-time algorithm that computes a kernel of size 36s^3k for Small Cycle Transversal. In order to achieve this kernel, we extend the region decomposition technique of Alber et al. (2004) [1] by considering a unique region decomposition… CONTINUE READING

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