A Tighter Erdős-Pósa Function for Long Cycles

@article{Fiorini2014ATE,
  title={A Tighter Erdős-P{\'o}sa Function for Long Cycles},
  author={Samuel Fiorini and Audrey Herinckx},
  journal={ArXiv},
  year={2014},
  volume={abs/1205.0940}
}
We prove that there exists a bivariate function f with f(k,l) = O(l k log k) such that for every naturals k and l, every graph G has at least k vertex-disjoint cycles of length at least l or a set of at most f(k,l) vertices that meets all cycles of length at least l. This improves a result by Birmel\'e, Bondy and Reed (Combinatorica, 2007), who proved the same result with f(k,l) = \Theta(l k^2). 

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Graph theory, volume 173 of Graduate Texts in Mathematics
  • Graph theory, volume 173 of Graduate Texts in Mathematics
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Reed . The ErdősPósa property for long circuits
  • Combinatorica
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Department of Mathematics CP 216, Boulevard du Triomphe, B-1050 Brussels
  • Department of Mathematics CP 216, Boulevard du Triomphe, B-1050 Brussels