M. Abu-ata and F. Dragan, Metric tree-like structures in real-world networks: an empirical study. Networks, vol.67, pp.49-68, 2016.

J. Andrade, H. Herrmann, R. Andrade, and L. Da-silva, Apollonian networks: Simultaneously scale-free, small world, euclidean, space filling, and with matching graphs, Phys. Rev. Lett, vol.94, 2005.

S. Arnborg, D. Corneil, and A. Proskurowski, Complexity of finding embeddings in a k-tree, SIAM Journal on Algebraic Discrete Methods, vol.8, issue.2, pp.277-284, 1987.

R. Belmonte, F. V. Fomin, P. A. Golovach, and M. S. Ramanujan, Metric dimension of bounded tree-length graphs, SIAM J. Discrete Math, vol.31, issue.2, pp.1217-1243, 2017.

A. Berry, R. Pogorelcnik, and A. Sigayret, Vertical decomposition of a lattice using clique separators, CLA'11, pp.15-29, 2011.

A. Berry, R. Pogorelcnik, and G. Simonet, An introduction to clique minimal separator decomposition, Algorithms, vol.3, issue.2, pp.197-215, 2010.
URL : https://hal.archives-ouvertes.fr/lirmm-00485851

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

H. Bodlaender, Treewidth: Characterizations, applications, and computations, WG 2006, pp.1-14, 2006.

H. Bodlaender, M. Fellows, and T. Warnow, Two strikes against perfect phylogeny, ICALP'92, pp.273-283, 1992.

H. Bodlaender and T. Kloks, Efficient and constructive algorithms for the pathwidth and treewidth of graphs, Journal of Algorithms, vol.21, issue.2, pp.358-402, 1996.

H. L. Bodlaender and A. Koster, Safe separators for treewidth, Discrete Mathematics, vol.306, issue.3, pp.337-350, 2006.

V. Bouchitté and I. Todinca, Listing all potential maximal cliques of a graph, Theoretical Computer Science, vol.276, issue.1, pp.17-32, 2002.

A. Brandstädt, F. Dragan, V. Chepoi, and V. Voloshin, Dually chordal graphs, SIAM Journal on Discrete Mathematics, vol.11, issue.3, pp.437-455, 1998.

S. Chechik, D. Larkin, L. Roditty, G. Schoenebeck, R. Tarjan et al., Better approximation algorithms for the graph diameter, ACM SODA'14, pp.1041-1052, 2014.

V. Chepoi, F. Dragan, B. Estellon, M. Habib, and Y. Vaxès, Diameters, centers, and approximating trees of ?-hyperbolic geodesic spaces and graphs, SCG '08, pp.59-68, 2008.

D. Coudert, G. Ducoffe, and N. Nisse, To approximate treewidth, use treelength! SIAM Journal of Discrete Mathematics, vol.30, issue.3, pp.1424-1436, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01348965

F. De-montgolfier, M. Soto, and L. Viennot, Treewidth and hyperbolicity of the internet, Network Computing and Applications (NCA), pp.25-32, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00909736

Y. Dourisboure, F. Dragan, C. Gavoille, and Y. Chenyu, Spanners for bounded tree-length graphs, Theor. Comput. Sci, vol.383, issue.1, pp.34-44, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00369676

Y. Dourisboure and C. Gavoille, Tree-decompositions with bags of small diameter, Discrete Mathematics, vol.307, issue.16, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00307800

F. Dragan and M. Abu-ata, Collective additive tree spanners of bounded tree-breadth graphs with generalizations and consequences, Theoretical Computer Science, vol.547, pp.1-17, 2014.

F. Dragan and E. Köhler, An approximation algorithm for the tree t-spanner problem on unweighted graphs via generalized chordal graphs, Algorithmica, vol.69, issue.4, pp.884-905, 2014.

F. Dragan, E. Köhler, and A. Leitert, Line-distortion, bandwidth and path-length of a graph, Algorithm Theory-SWAT 2014, pp.158-169, 2014.

F. Dragan and A. Leitert, On the minimum eccentricity shortest path problem, Algorithms and Data Structures -WADS, pp.276-288, 2015.

G. Ducoffe, A short note on the complexity of computing strong pathbreadth
URL : https://hal.archives-ouvertes.fr/hal-01735826

G. Ducoffe, N. Legay, and N. Nisse, On the complexity of computing treebreadth, IWOCA 2016 -27th International Workshop on Combinatorial Algorithms, pp.3-15, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01354996

G. Ducoffe, S. Legay, and N. Nisse, On computing tree and path decompositions with metric constraints on the bags, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01254917

F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, Journal of Combinatorial Theory, Series B, vol.16, issue.1, pp.47-56, 1974.

M. Golumbic, H. Kaplan, and R. Shamir, On the complexity of dna physical mapping, Advances in Applied Mathematics, vol.15, issue.3, pp.251-261, 1994.

M. C. Golumbic, Algorithmic graph theory and perfect graphs, vol.57, 2004.

R. Krauthgamer and J. Lee, Algorithms on negatively curved spaces, FOCS'06, pp.119-132, 2006.

A. Leitert, 3-colouring for dually chordal graphs and generalisations, Information Processing Letters, vol.128, pp.21-26, 2017.

A. Leitert and F. Dragan, On strong tree-breadth, International Conference on Combinatorial Optimization and Applications, pp.62-76, 2016.

D. Lokshtanov, On the complexity of computing treelength, Discrete Applied Mathematics, vol.158, issue.7, pp.820-827, 2010.

G. Mertzios and P. Spirakis, Algorithms and almost tight results for 3-colorability of small diameter graphs, International Conference on Current Trends in Theory and Practice of Computer Science, pp.332-343, 2013.

J. Opatrny, Total ordering problem, SIAM J. Comput, vol.8, issue.1, pp.111-114, 1979.

A. Parra and P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics, vol.79, issue.1, pp.171-188, 1997.

N. Robertson and P. Seymour, Graph minors. II. algorithmic aspects of tree-width, Journal of algorithms, vol.7, issue.3, pp.309-322, 1986.

C. Wang, T. Liu, W. Jiang, and K. Xu, Feedback vertex sets on tree convex bipartite graphs, COCOA 2012, pp.95-102, 2012.

Y. Wu, P. Austrin, T. Pitassi, and D. Liu, Inapproximability of treewidth and related problems, J. Artif. Intell. Res. (JAIR), vol.49, pp.569-600, 2014.