S. Arnborg, D. G. Corneil, and A. Proskurowski, -Tree, SIAM Journal on Algebraic Discrete Methods, vol.8, issue.2, pp.277-284, 1987.
DOI : 10.1137/0608024

[. Bandelt and V. Chepoi, Metric graph theory and geometry: a survey, Contemporary Mathematics, vol.453, pp.49-86, 2008.
DOI : 10.1090/conm/453/08795

L. Hans, P. G. Bodlaender, M. S. Drange, F. V. Dregi, D. Fomin et al., A o(c k n) 5-approximation algorithm for treewidth, 2013.

L. Hans and . Bodlaender, Dynamic programming on graphs with bounded treewidth, 15th International Colloquium on Automata, Languages and Programming (ICALP), pp.105-118, 1988.

L. Hans and . Bodlaender, Dynamic algorithms for graphs with treewidth 2, 19th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pp.112-124, 1993.

L. Hans and . Bodlaender, A linear-time algorithm for finding tree-decompositions of small treewidth, SIAM J. Comput, vol.25, issue.6, pp.1305-1317, 1996.

M. Boguna, F. Papadopoulos, and D. Krioukov, Sustaining the Internet with hyperbolic mapping, Nature Communications, vol.16, issue.6, pp.1-18, 2010.
DOI : 10.1038/ncomms1063

D. [. Cohen, A. Coudert, and . Lancin, Exact and approximate algorithms for computing the hyperbolicity of large-scale graphs, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00735481

F. F. Victor-chepoi, B. Dragan, M. Estellon, Y. Habib, Y. Vaxès et al., Additive spanners and distance and routing labeling schemes for hyperbolic graphs, Algorithmica, pp.62-65, 2012.

B. [. Chepoi and . Estellon, Packing and Covering ??-Hyperbolic Spaces by Balls, Approximation , Randomization, and Combinatorial Optimization. Algorithms and Techniques, pp.59-73, 2007.
DOI : 10.1007/978-3-540-74208-1_5

B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Information and Computation, vol.85, issue.1, pp.12-75, 1990.
DOI : 10.1016/0890-5401(90)90043-H
URL : https://hal.archives-ouvertes.fr/hal-00353765

Y. Dourisboure and C. Gavoille, Tree-decompositions with bags of small diameter, Discrete Mathematics, vol.307, issue.16, pp.2008-2029, 2007.
DOI : 10.1016/j.disc.2005.12.060
URL : https://hal.archives-ouvertes.fr/hal-00307800

[. Dieng and C. Gavoille, On the Tree-Width of Planar Graphs, Electronic Notes in Discrete Mathematics, vol.34, pp.593-596, 2009.
DOI : 10.1016/j.endm.2009.07.099
URL : https://hal.archives-ouvertes.fr/hal-00408481

E. D. Demaine and M. Hajiaghayi, The Bidimensionality Theory and Its Algorithmic Applications, The Computer Journal, vol.51, issue.3, pp.292-302, 2008.
DOI : 10.1093/comjnl/bxm033

E. D. Demaine, M. Hajiaghayi, and D. M. Thilikos, The Bidimensional Theory of Bounded-Genus Graphs, SIAM Journal on Discrete Mathematics, vol.20, issue.2, pp.357-371, 2006.
DOI : 10.1137/040616929

Y. Dieng, Décomposition arborescente des graphes planaires et routage compact, 2009.

R. Diestel and M. Müller, Connected tree-width, nov 2014
DOI : 10.1007/s00493-016-3516-5

]. F. De-montgolfier, M. Soto, and L. Viennot, Treewidth and Hyperbolicity of the Internet, 2011 IEEE 10th International Symposium on Network Computing and Applications, pp.25-32, 2011.
DOI : 10.1109/NCA.2011.11
URL : https://hal.archives-ouvertes.fr/hal-00909736

Y. Dourisboure, Compact Routing Schemes for Generalised Chordal Graphs, Journal of Graph Algorithms and Applications, vol.9, issue.2, pp.277-297, 2005.
DOI : 10.7155/jgaa.00109

P. Duchet, M. L. Vergnas, and H. Meyniel, Connected cutsets of a graph and triangle bases of the cycle space, Discrete Mathematics, vol.62, issue.2, pp.145-154, 1986.
DOI : 10.1016/0012-365X(86)90115-9

V. Fedor, P. A. Fomin, D. M. Golovach, and . Thilikos, Contraction obstructions for treewidth, J. Comb. Theory, Ser. B, vol.101, issue.5, pp.302-314, 2011.

U. Feige, M. Hajiaghayi, and J. R. Lee, Improved Approximation Algorithms for Minimum Weight Vertex Separators, SIAM Journal on Computing, vol.38, issue.2, pp.629-657, 2008.
DOI : 10.1137/05064299X

A. [. Fournier, A. Ismail, and . Vigneron, Computing the Gromov hyperbolicity of a discrete metric space, Information Processing Letters, vol.115, issue.6-8, 2012.
DOI : 10.1016/j.ipl.2015.02.002

P. Galinier, M. Habib, and C. Paul, Chordal graphs and their clique graphs, 21st International Workshop on Graph-Theoretic Concepts in Computer Science (WG '95), pp.358-371, 1995.
DOI : 10.1007/3-540-60618-1_88
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.9635

]. M. Gro87 and . Gromov, Hyperbolic groups. Essays in Group Theory, pp.75-263, 1987.

T. Jiang, S. Kim, B. Douglas, and . West, Isometric cycles, cutsets, and crowning of bridged graphs, Journal of Graph Theory, vol.622, issue.3, pp.161-170, 2003.
DOI : 10.1002/jgt.10110

J. [. Krauthgamer and . Lee, Algorithms on negatively curved spaces, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06), pp.119-132, 2006.
DOI : 10.1109/FOCS.2006.9

D. Lokshtanov, Finding the longest isometric cycle in a graph, Discrete Applied Mathematics, vol.157, issue.12, pp.2670-2674, 2009.
DOI : 10.1016/j.dam.2008.08.008

D. Lokshtanov, On the complexity of computing treelength, Discrete Applied Mathematics, vol.158, issue.7, pp.820-827, 2010.
DOI : 10.1016/j.dam.2009.10.007

A. Parra and P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics, vol.79, issue.1-3, pp.171-188, 1997.
DOI : 10.1016/S0166-218X(97)00041-3

N. Robertson and P. D. Seymour, Graph minors ??? a survey, Surveys in combinatorics 1985, pp.153-171, 1985.
DOI : 10.1017/CBO9781107325678.009

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

D. Paul, R. Seymour, and . Thomas, Call routing and the ratcatcher, Combinatorica, vol.14, issue.2, pp.217-241, 1994.