A 4k2 kernel for feedback vertex set

@article{Thomass2010A4K,
  title={A 4k2 kernel for feedback vertex set},
  author={St{\'e}phan Thomass{\'e}},
  journal={ACM Trans. Algorithms},
  year={2010},
  volume={6},
  pages={32:1-32:8}
}
We prove that given an undirected graph <i>G</i> on <i>n</i> vertices and an integer <i>k</i>, one can compute, in polynomial time in <i>n</i>, a graph <i>G′</i> with at most 4<i>k</i><sup>2</sup> vertices and an integer <i>k′</i> such that <i>G</i> has a feedback vertex set of size at most <i>k</i> iff <i>G′</i> has a feedback vertex set of size at most <i>k′</i>. This result improves a previous <i>O</i>(<i>k</i><sup>11</sup>) kernel of Burrage et al., and a more recent cubic kernel of… CONTINUE READING

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