Packing cycles through prescribed vertices

@article{Kakimura2011PackingCT,
  title={Packing cycles through prescribed vertices},
  author={Naonori Kakimura and K. Kawarabayashi and D. Marx},
  journal={J. Comb. Theory, Ser. B},
  year={2011},
  volume={101},
  pages={378-381}
}
The well-known theorem of Erdos and Posa says that a graph G has either k vertex-disjoint cycles or a vertex set X of order at most f(k) such that [email protected]?X is a forest. Starting with this result, there are many results concerning packing and covering cycles in graph theory and combinatorial optimization. In this paper, we generalize [email protected]?s result to cycles that are required to go through a set S of vertices. Given an integer k and a vertex subset S (possibly unbounded… Expand
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