The Erdős–Pósa Property For Long Circuits

We show that, for every l, the family \( \mathcal{F}_{l} \) of circuits of length at least l satisfies the Erdős–Pósa property, with f(k)=13l(k−1)(k−2)+(2l+3)(k−1), thereby sharpening a result of C. Thomassen. We obtain as a corollary that graphs without k disjoint circuits of length l or more have tree-width O(lk2).

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Correspondence to Etienne Birmelé.

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Birmelé, E., Bondy, J.A. & Reed, B.A. The Erdős–Pósa Property For Long Circuits. Combinatorica 27, 135–145 (2007).

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Mathematics Subject Classification (2000):

  • 05C35
  • 05C38
  • 05C83