Abstract
For an integer ℓ at least 3, we prove that if G is a graph containing no two vertex-disjoint circuits of length at least ℓ, then there is a set X of at most
vertices that intersects all circuits of length at least ℓ. Our result improves the bound 2ℓ + 3 due to Birmelé, Bondy, and Reed (The Erdős-Pósa property for long circuits, Combinatorica 27 (2007), 135–145) who conjecture that ℓ vertices always suffice.
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References
E. Birmelé, Thèse de doctorat, Université de Lyon 1, 2003.
E. Birmelé, J. A. Bondy and B. A. Reed, The Erdős-Pósa property for long circuits, Combinatorica 27 (2007), 135–145.
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© 2013 Scuola Normale Superiore Pisa
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Meierling, D., Rautenbach, D., Sasse, T. (2013). The Erdős-Pósa property for long circuits. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_4
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DOI: https://doi.org/10.1007/978-88-7642-475-5_4
Publisher Name: Edizioni della Normale, Pisa
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