E. Birmelé, J. A. Bondy, and B. A. Reed, The Erd??s???P??sa Property For Long Circuits, Combinatorica, vol.27, issue.2, pp.135-145, 2007.
DOI : 10.1007/s00493-007-0047-0

L. Hans, A. M. Bodlaender, T. Koster, and . Wolle, Contraction and treewidth lower bounds, Algorithms ? ESA 2004, pp.628-639, 2004.

L. Hans, R. B. Bodlaender-van-leeuwen, D. M. Tan, and . Thilikos, On interval routing schemes and treewidth, Inf. Comput, vol.139, issue.1, pp.92-109, 1997.

C. Chekuri and J. Chuzhoy, Large-treewidth graph decompositions and applications, Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, STOC '13, p.2013, 2013.
DOI : 10.1145/2488608.2488645

R. Diestel, Graph Theory, volume 173 of Graduate Texts in Mathematics, 2010.

R. Diestel, T. R. Jensen, K. Y. Gorbunov, and C. Thomassen, Highly Connected Sets and the Excluded Grid Theorem, Journal of Combinatorial Theory, Series B, vol.75, issue.1, pp.61-73, 1999.
DOI : 10.1006/jctb.1998.1862

P. Erd?-os and G. Szekeres, A combinatorial problem in geometry, Classic Papers in Combinatorics, Modern Birkhäuser Classics, pp.49-56, 1987.

P. Erd?, O. , and L. Pósa, On independent circuits contained in a graph, Canad. J. Math, vol.17, pp.347-352, 1965.

S. Fiorini, G. Joret, and I. Sau, Optimal Erd? os?Pósa property for pumpkins, 2013.

V. Fedor, D. Fomin, N. Lokshtanov, G. Misra, S. Philip et al., Quadratic upper bounds on the erd? os?pósa property for a generalization of packing and covering cycles, Journal of Graph Theory

V. Fedor, S. Fomin, D. M. Saurabh, and . Thilikos, Strengthening Erd? os?Pósa property for minor-closed graph classes, Journal of Graph Theory, vol.66, issue.3, pp.235-240, 2011.

J. Geelen and K. Kabell, The Erd??s???P??sa property for matroid circuits, Journal of Combinatorial Theory, Series B, vol.99, issue.2, pp.407-419, 2009.
DOI : 10.1016/j.jctb.2008.08.004

K. Ichi, K. , and Y. Kobayashi, Linear min-max relation between the treewidth of H-minor-free graphs and its largest grid, 29th Int. Symposium on Theoretical Aspects of Computer Science Schloss Dagstuhl?Leibniz-Zentrum für Informatik, pp.278-289, 2012.

A. V. Kostochka, Lower bound of the hadwiger number of graphs by their average degree, Combinatorica, vol.7, issue.4, pp.307-316, 1984.
DOI : 10.1007/BF02579141

A. Leaf and P. Seymour, Treewidth and planar minors, 2012.

J. Raymond and D. M. Thilikos, Low Polynomial Exclusion of Planar Graph Patterns, Journal of Graph Theory, vol.62, issue.2, 2013.
DOI : 10.1002/jgt.22009

URL : https://hal.archives-ouvertes.fr/lirmm-01263767

N. Robertson and P. D. Seymour, Graph minors. V. Excluding a planar graph, Journal of Combinatorial Theory, Series B, vol.41, issue.1, pp.92-114, 1986.
DOI : 10.1016/0095-8956(86)90030-4

URL : http://doi.org/10.1006/jctb.1999.1919

R. W. David, G. Samuel-fiorini, and . Joret, Excluded forest minors and the Erd? os-Pósa property, p.2012

M. Stiebitz, Decomposing graphs under degree constraints, Journal of Graph Theory, vol.23, issue.3, pp.321-324, 1996.
DOI : 10.1002/(SICI)1097-0118(199611)23:3<321::AID-JGT12>3.0.CO;2-H

A. Thomason, The Extremal Function for Complete Minors, Journal of Combinatorial Theory, Series B, vol.81, issue.2, pp.318-338, 2001.
DOI : 10.1006/jctb.2000.2013