Distortion of the hyperbolicity constant of a graph

Electronic Journal of Combinatorics

Volumn 19, Issue , 2012, Pages 1-18

  Carballosa, Walter ^a   Pestana, Domingo ^a   Rodríguez, José M ^a   Sigarreta, José M ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE GUERRERO   (Mexico)

Author keywords

Edges; Geodesics; Gromov hyperbolicity; Infinite graphs

Indexed keywords

EID: 84860112680     PISSN: None     EISSN: 10778926     Source Type: Journal    
DOI: 10.37236/2175     Document Type: Article

References (34)

1. Bermudo, S., Rodríguez, J. M. and Sigarreta, J. M., Computing the hyperbolicity constant, Comput. Math. Appl. 62 (12) (2011), 4592-4595.
2. Bermudo, S., Rodríguez, J. M., Sigarreta, J. M. and Vilaire, J.-M., Mathematical properties of Gromov hyperbolic graphs, AIP Conference Proceedings, Vol. 1281 (2010), 575-578.
3. Bermudo, S., Rodríguez, J. M., Sigarreta, J. M. and Vilaire, J.-M., Gromov hyperbolic graphs. Submitted.
4. Bermudo, S., Rodríguez, J. M., Sigarreta, J. M. and Tourís, E., Hyperbolicity and complement of graphs, Appl. Math. Letters 24 (2011), 1882-1887.
5. Bowditch, B. H., Notes on Gromov's hyperobolicity criterion for path-metric spaces. Group theory from a geometrical viewpoint, Trieste, 1990 (ed. E. Ghys, A. Haefliger and A. Verjovsky; World Scientific, River Edge, NJ, 1991) 64-167.
6. Brinkmann, G., Koolen J. and Moulton, V., On the hyperbolicity of chordal graphs, Ann. Comb. 5 (2001), 61-69.
7. Carballosa, W., Portilla, A., Rodríguez, J. M. and Sigarreta, J. M., Gromov hyperbolicity of planar graphs and CW complexes. Submitted.
8. Carballosa, W., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., On the hyperbolicity constant of line graphs, Electr. J. Comb. 18 (2011), #P210.
9. Chen, B., Yau, S.-T., Yeh, Y.-N., Graph homotopy and Graham homotopy, Discrete Math. 241 (2001), 153-170.
10. Chepoi, V., Dragan, F. F., Estellon, B., Habib, M. and Vaxes Y., Notes on diameters, centers, and approximating trees of -hyperbolic geodesic spaces and graphs, Electr. Notes Discrete Math. 31 (2008), 231-234.
11. Frigerio, R. and Sisto, A., Characterizing hyperbolic spaces and real trees, Geom Dedicata 142 (2009), 139-149.
12. Ghys, E. and de la Harpe, P., Sur les Groupes Hyperboliques d'après Mikhael Gromov. Progress in Mathematics 83, Birkhäuser Boston Inc., Boston, MA, 1990.
13. Gromov, M., Hyperbolic groups, in Essays in group theory. Edited by S. M. Gersten, M. S. R. I. Publ. 8. Springer, 1987, 75-263.
14. Gromov, M. (with appendices by M. Katz, P. Pansu and S. Semmes), Metric Structures for Riemannian and Non-Riemannnian Spaces. Progress in Mathematics, vol. 152. Birkhäuser, 1999.
15. Jonckheere, E. and Lohsoonthorn, P., A hyperbolic geometry approach to multipath routing, Proceedings of the 10th Mediterranean Conference on Control and Automation (MED 2002), Lisbon, Portugal, July 2002. FA5-1.
16. Jonckheere, E. A., Controle du trafic sur les reseaux a geometrie hyperbolique-Une approche mathematique a la securite de l'acheminement de l'information, Journal Europeen de Systemes Automatises 37(2) (2003), 145-159.
17. Jonckheere, E. A. and Lohsoonthorn, P., Geometry of network security, American Control Conference ACC (2004), 111-151.
18. Jonckheere, E. A., Lohsoonthorn, P. and Ariaesi, F, Upper bound on scaled Gromovhyperbolic delta, Applied Mathematics and Computation 192 (2007), 191-204.
19. Jonckheere, E. A., Lohsoonthorn, P. and Bonahon, F., Scaled Gromov hyperbolic graphs, Journal of Graph Theory 2 (2007), 157-180.
20. Koolen, J. H. and Moulton, V., Hyperbolic Bridged Graphs, Europ. J. Combinatorics 23 (2002), 683-699.
21. Michel, J., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., Hyperbolicity and parameters of graphs, Ars Comb. Volume C (2011), 43-63.
22. Michel, J., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., Gromov hyperbolicity in cartesian product graphs, Proc. Indian Acad. Sci. Math. Sci. 120 (2010), 1-17.
23. Oshika, K., Discrete groups, AMS Bookstore, 2002.
24. Pestana, D., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., Gromov hyperbolic cubic graphs. To appear in Central European J. Math. DOI 10.2478/s11533-012-0036-4
25. Portilla, A., Rodríguez, J. M., Sigarreta, J. M. and Vilaire, J.-M., Gromov hyperbolic tessellation graphs. To appear in Utilitas Math.
26. Portilla, A., Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity through decomposition of metric spaces II, J. Geom. Anal. 14 (2004), 123-149.
27. Portilla, A., Rodríguez, J. M. and Tourís, E., Stability of Gromov hyperbolicity, J. Advan. Math. Studies 2 (2009), 77-96.
28. Portilla, A. and Tourís, E., A characterization of Gromov hyperbolicity of surfaces with variable negative curvature, Publ. Mat. 53 (2009), 83-110.
29. Rodríguez, J. M. and Sigarreta, J. M., Bounds on Gromov hyperbolicity constant in graphs. Proc. Indian Acad. Sci. Math. Sci. 122 (2012), 5365.
30. Rodríguez, J. M., Sigarreta, J. M., Vilaire, J.-M. and Villeta, M., On the hyperbolicity constant in graphs, Discrete Math. 311 (2011), 211-219.
31. Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity through decomposition of metric spaces, Acta Math. Hung. 103 (2004), 53-84.
32. Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity of Riemann surfaces, Acta Math. Sinica 23 (2007), 209-228.
33. Tourís, E., Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces, J. Math. Anal. Appl. 380 (2011), 865-881.
34. Wu, Y., Zhang, C., Chordality and hyperbolicity of a graph, Electr. J. Comb. 18 (2011), #P43.