On the hyperbolicity constant in graphs

Discrete Mathematics

Volumn 311, Issue 4, 2011, Pages 211-219

  Rodríguez, José M ^a   Sigarreta, José M ^b   Vilaire, Jean Marie ^a   Villeta, María ^c  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b Universidad Autanoma de Guerrero   (Mexico)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Connectivity; Geodesics; Graphs; Gromov Hyperbolicity

Indexed keywords

EID: 79953800557     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2010.11.005     Document Type: Article

References (41)

1. V. Alvarez, A. Portilla, J.M. Rodrguez, and E. Tours Gromov hyperbolicity of Denjoy domains Geom. Dedicata 121 2006 221 245
2. S. Bermudo, H. Fernau, J.M. Rodrguez, J.M. Sigarreta, Discretization of the hyperbolicity constant. Preprint.
3. S. Bermudo, J.M. Rodrguez, J.M. Sigarreta, and J.-M. Vilaire Mathematical properties of Gromov hyperbolic graphs AIP Conf. Proc. 281 2010 575 578
4. S. Bermudo, J.M. Rodrguez, J.M. Sigarreta, J.-M. Vilaire, Gromov hyperbolic Graphs (submitted for publication).
5. S. Bermudo, J.M. Rodrguez, J.M. Sigarreta, E. Tours, Hyperbolicity and complement of graphs (submitted for publication).
6. Z.M. Balogh, and M. Bonk Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains Comment. Math. Helv. 75 2000 504 533
7. Z.M. Balogh, and S.M. Buckley Geometric characterizations of Gromov hyperbolicity Invent. Math. 153 2003 261 301 (Pubitemid 36931521)
8. Y. Benoist Convexes hyperboliques et fonctions quasisymtriques Publ. Math. Inst. Hautes tudes Sci. 97 2003 181 237
9. M. Bonk Quasi-geodesics segments and Gromov hyperbolic spaces Geom. Dedicata 62 1996 281 298 (Pubitemid 126716455)
10. M. Bonk, J. Heinonen, and P. Koskela Uniformizing Gromov hyperbolic spaces Astrisque 270 2001
11. M. Bonk, and O. Schramm Embeddings of Gromov hyperbolic spaces Geom. Funct. Anal. 10 2000 266 306
12. B.H. Bowditch Notes on Gromov's hyperobolicity criterion for path-metric spaces E. Ghys, A. Haefliger, A. Verjovsky, Group Theory from a Geometrical Viewpoint, Trieste, 1990 1991 World Scientific River Edge, NJ 64 167
13. G. Brinkmann, J. Koolen, and V. Moulton On the hyperbolicity of chordal graphs Ann. Comb. 5 2001 61 69
14. R. Frigerio, and A. Sisto Characterizing hyperbolic spaces and real trees Geom. Dedicata 142 2009 139 149
15. G. Gavoille, and O. Ly Distance labeling in hyperbolic graphs Lect. Notes Comput. Sci. 3827 2005 1071 1079 (Pubitemid 43856332)
16. E. Ghys, and P. de la Harpe Sur les groupes hyperboliques d'aprs Mikhael Gromov Progress in Mathematics 83 1990 Birkhuser Boston Inc Boston, MA
17. G metrics Proc. Amer. Math. Soc. 134 2006 1137 1142
18. P.A. Hst, H. Lindn, A. Portilla, J.M. Rodrguez, E. Tours, Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics, J. Math. Soc. Japan (in press).
19. P.A. Hst, A. Portilla, J.M. Rodrguez, and E. Tours Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains Bull. London Math. Soc. 42 2010 282 294
20. P.A. Hst, A. Portilla, J.M. Rodrguez, and E. Tours Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics Complex Var. Elliptic Equ. 55 2010 127 135
21. P.A. Hst, A. Portilla, J.M. Rodrguez, E. Tours, Uniformly separated sets and Gromov hyperbolicity of domains with the quasihyperbolic metric. Medit. J. Math. in press, (doi:10.1007/s00009-010-0059-7 ).
22. E. Jonckheere, P. Lohsoonthorn, A hyperbolic geometry approach to multipath routing, in: Proceedings of the 10th Mediterranean Conference on Control and Automation, MED 2002, Lisbon, Portugal, July, 2002. FA5-1.
23. E.A. Jonckheere Contrle du trafic sur les rseaux gometrie hyperboliqueUne approche mathmatique a la scurit de l'acheminement de l'information J. Europen de Systmes Automatiss 37 2 2003 145 159
24. E.A. Jonckheere, P. Lohsoonthorn, Geometry of network security, in: American Control Conference, ACC, 2004, pp. 111151.
25. E.A. Jonckheere, P. Lohsoonthorn, and F. Ariaesi Upper bound on scaled Gromov-hyperbolic delta Appl. Math. Comput. 192 2007 191 204 (Pubitemid 47362310)
26. E.A. Jonckheere, P. Lohsoonthorn, and F. Bonahon Scaled Gromov hyperbolic graphs J. Graph Theory 2 2007 157 180 (Pubitemid 351213233)
27. A. Karlsson, and G.A. Noskov The Hilbert metric and Gromov hyperbolicity Enseign. Math. 48 2002 73 89
28. H. Lindn Gromov hyperbolicity of certain conformal invariant metrics Ann. Acad. Sci. Fenn. Math. 32 1 2007 279 288
29. J.H. Koolen, and V. Moulton Hyperbolic bridged graphs European J. Combin. 23 2002 683 699 (Pubitemid 39659438)
30. K. Matsuzaki, J.M. Rodrguez, Twists and Gromov hyperbolicity of Riemann surfaces, Acta Math. Sinica (in press).
31. J. Michel, J.M. Rodrguez, J.M. Sigarreta, M. Villeta, Hyperbolicity and parameters of graphs, Ars Combin. (in press).
32. J. Michel, J.M. Rodrguez, J.M. Sigarreta, and M. Villeta Gromov hyperbolicity in cartesian product graphs Proc. Indian Acad. Sci. Math. Sci. 120 5 2010 1 17
33. K. Oshika Discrete Groups 2002 AMS Bookstore
34. A. Portilla, J.M. Rodrguez, and E. Tours Gromov hyperbolicity through decomposition of metric spaces II J. Geom. Anal. 14 2004 123 149
35. A. Portilla, J.M. Rodrguez, and E. Tours Stability of Gromov hyperbolicity J. Adv. Math Stud. 2 2009 1 20
36. A. Portilla, and E. Tours A characterization of Gromov hyperbolicity of surfaces with variable negative curvature Publ. Mat. 53 2009 83 110
37. J.M. Rodrguez, and E. Tours Gromov hyperbolicity through decomposition of metric spaces Acta Math. Hung. 103 2004 53 84
38. J.M. Rodrguez, and E. Tours A new characterization of Gromov hyperbolicity for Riemann surfaces Publ. Mat. 50 2006 249 278
39. J.M. Rodrguez, and E. Tours Gromov hyperbolicity of Riemann surfaces Acta Math. Sinica 23 2007 209 228
40. E. Tours, Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces, J. Math. Anal. Appl. (in press).
41. Y. Wu, C. Zhang, Chordality and hyperbolicity of a graph (submitted for publication).