S. Bezrukov, R. Elsässer, B. Monien, R. Preis, and J. Tillich, New spectral lower bounds on the bisection width of graphs, Theoretical Computer Science, vol.320, pp.2-3155, 2004.

D. Bienstock, N. Robertson, P. Seymour, and R. Thomas, Quickly excluding a forest, Journal of Combinatorial Theory, Series B, vol.52, issue.2, pp.274-283, 1991.
DOI : 10.1016/0095-8956(91)90068-U

N. Biggs and A. Boshier, Note on the girth of Ramanujan graphs, Journal of Combinatorial Theory, Series B, vol.49, issue.2, pp.190-194, 1990.
DOI : 10.1016/0095-8956(90)90026-V

E. Birmelé, J. Bondy, and B. Reed, Brambles, Prisms and Grids, Graph Theory in Paris, pp.37-44, 2007.
DOI : 10.1007/978-3-7643-7400-6_4

L. Hans and . Bodlaender, On linear time minor tests with depth-first search, J. Algorithms, vol.14, issue.1, pp.1-23, 1993.

L. Hans and . Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Theoret. Comput. Sci, vol.209, issue.12, pp.1-45, 1998.

L. Hans, D. M. Bodlaender, and . Thilikos, Computing small search numbers in linear time, Proceedings of the First International Workshop on Parameterized and Exact Computation, pp.37-48, 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, Polynomial bounds for the grid-minor theorem. CoRR, abs/1305, 2013.

E. D. Demaine and M. Hajiaghayi, Linearity of grid minors in treewidth with applications through bidimensionality, Combinatorica, vol.14, issue.2, pp.19-36, 2008.
DOI : 10.1007/s00493-008-2140-4

E. D. Demaine, M. Hajiaghayi, and K. Kawarabayashi, Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner???s Contraction, Algorithmica, vol.9, issue.6, pp.142-180, 2009.
DOI : 10.1007/s00453-007-9138-y

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.

R. Michael, M. A. Fellows, and . Langston, On search, decision, and the efficiency of polynomial-time algorithms, J. Comput. System Sci, vol.49, issue.3, pp.769-779, 1994.

V. Fedor, D. Fomin, S. Lokshtanov, and . Saurabh, Bidimensionality and geometric graphs, 23st ACM?SIAM Symposium on Discrete Algorithms, 2012.

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

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

M. Morgenstern, Existence and Explicit Constructions of q + 1 Regular Ramanujan Graphs for Every Prime Power q, Journal of Combinatorial Theory, Series B, vol.62, issue.1, pp.44-62, 1994.
DOI : 10.1006/jctb.1994.1054

A. Proskurowski, Maximal Graphs of Path-width K Or Searching a Partial K-caterpillar, 1989.

N. Robertson and P. D. Seymour, Graph minors. II. Algorithmic aspects of tree-width, Journal of Algorithms, vol.7, issue.3, pp.309-322, 1986.
DOI : 10.1016/0196-6774(86)90023-4
URL : http://doi.org/10.1006/jctb.1999.1919

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

N. Robertson, P. D. Seymour, and R. Thomas, Quickly Excluding a Planar Graph, Journal of Combinatorial Theory, Series B, vol.62, issue.2, pp.323-348, 1994.
DOI : 10.1006/jctb.1994.1073