Cycle transversals in perfect graphs and cographs

@article{Brandstdt2013CycleTI,
  title={Cycle transversals in perfect graphs and cographs},
  author={Andreas Brandst{\"a}dt and Synara Brito and Sulamita Klein and Loana Tito Nogueira and F{\'a}bio Protti},
  journal={Theor. Comput. Sci.},
  year={2013},
  volume={469},
  pages={15-23}
}
A cycle transversal (or feedback vertex set) of a graph G is a subset T ⊆ V (G) such that T ∩ V (C) ≠ ∅ for every cycle C of G. This work considers the problem of finding special cycle transversals in perfect graphs and cographs. We prove that finding a minimum cycle transversal T in a perfect graph G is NP-hard, even for bipartite graphs with maximum degree four. Since G−T is acyclic, this result implies that finding amaximum acyclic induced subgraph of a perfect graph is also NP-hard. Other… CONTINUE READING

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