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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
P. Erdős and L. Pósa, On independent circuits contained in a graph, Canad. J. Math. 17 (1965), 347–352.
L. Lovász, On graphs not containing independent circuits (Hungarian), Mat. Lapok 16 (1965), 289–299.
C. Thomassen, On the presence of disjoint subgraphs of a specified type, J. Graph Theory 12 (1988), 101–111.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2013 Scuola Normale Superiore Pisa
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-88-7642-475-5_4
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-474-8
Online ISBN: 978-88-7642-475-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)