Disjoint cycles intersecting a set of vertices

@article{Pontecorvi2012DisjointCI,
  title={Disjoint cycles intersecting a set of vertices},
  author={M. Pontecorvi and P. Wollan},
  journal={J. Comb. Theory, Ser. B},
  year={2012},
  volume={102},
  pages={1134-1141}
}
A classic theorem of Erdos and Posa states that there exists a constant c such that for all positive integers k and graphs G, either G contains k vertex disjoint cycles, or there exists a subset of at most cklogk vertices intersecting every cycle of G. We consider the following generalization of the problem: fix a subset S of vertices of G. An S-cycle is a cycle containing at least one vertex of S. We show that again there exists a constant c^' such that G either contains k disjoint S-cycles… Expand

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