Gromov hyperbolic graphs

Discrete Mathematics

Volumn 313, Issue 15, 2013, Pages 1575-1585

  Bermudo, Sergio ^a   Rodríguez, José M ^b   Sigarreta, José M ^c   Vilaire, Jean Marie ^b  

^a UNIVERSIDAD PABLO DE OLAVIDE   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^c UNIVERSIDAD AUTÓNOMA DE GUERRERO   (Mexico)

Author keywords

Connectivity; Geodesics; Graphs; Gromov hyperbolicity

Indexed keywords

EID: 84876922267     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2013.04.009     Document Type: Article

References (29)

1. Z.M. Balogh, and S.M. Buckley Geometric characterizations of Gromov hyperbolicity Invent. Math. 153 2003 261 301
2. S. Bermudo, J.M. Rodríguez, and J.M. Sigarreta Computing the hyperbolicity constant Comput. Math. Appl. 62 2011 4592 4595
3. S. Bermudo, J.M. Rodríguez, J.M. Sigarreta, and E. Tourís Hyperbolicity and complement of graphs Appl. Math. Lett. 24 2011 1882 1887
4. M. Bonk, J. Heinonen, and P. Koskela Uniformizing Gromov hyperbolic spaces Astérisque 270 2001
5. B.H. Bowditch Notes on Gromov's hyperbolicity 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
6. G. Brinkmann, J. Koolen, and V. Moulton On the hyperbolicity of chordal graphs Ann. Comb. 5 2001 61 69
7. W. Carballosa, D. Pestana, J.M. Rodríguez, and J.M. Sigarreta Distortion of the hyperbolicity constant of a graph Electron. J. Combin. 19 2012 P67
8. W. Carballosa, J.M. Rodríguez, J.M. Sigarreta, and M. Villeta Gromov hyperbolicity of line graphs Electron. J. Combin. 18 2011 P210
9. R. Frigerio, and A. Sisto Characterizing hyperbolic spaces and real trees Geom. Dedicata 142 2009 139 149
10. E. Ghys, and P. de la Harpe Sur les Groupes Hyperboliques d'après Mikhael Gromov Progress in Mathematics vol. 83 1990 Birkhäuser Boston Inc. Boston, MA
11. G metrics Proc. Amer. Math. Soc. 134 2006 1137 1142
12. P.A. Hästö, A. Portilla, J.M. Rodríguez, and E. Tourís Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains Bull. London Math. Soc. 42 2010 282 294
13. P.A. Hästö, A. Portilla, J.M. Rodríguez, and E. Tourís Uniformly separated sets and Gromov hyperbolicity of domains with the quasihyperbolic metric Mediterr. J. Math. 8 2011 47 65
14. E.A. Jonckheere Contrôle du traffic sur les réseaux à géométrie hyperbolique-Vers une théorie géométrique de la sécurité l'acheminement de l'information J. Eur. Syst. Autom. 8 2002 45 60
15. 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.
16. E.A. Jonckheere, P. Lohsoonthorn, Geometry of network security, in: Amer. Control Conf., ACC, 2004, pp. 111-151.
17. M. Kanai Rough isometries and combinatorial approximations of geometries of noncompact Riemannian manifolds J. Math. Soc. Japan 37 1985 391 413
18. J.H. Koolen, and V. Moulton Hyperbolic bridged graphs Electron. J. Combin. 23 2002 683 699
19. J. Michel, J.M. Rodríguez, J.M. Sigarreta, and M. Villeta Gromov hyperbolicity in cartesian product graphs Proc. Indian Acad. Sci. Math. Sci. 120 2010 1 17
20. K. Oshika Discrete Groups 2002 AMS Bookstore
21. D. Pestana, J.M. Rodríguez, J.M. Sigarreta, and M. Villeta Gromov hyperbolic cubic graphs Cent. Eur. J. Math. 10 3 2012 1141 1151
22. A. Portilla, J.M. Rodríguez, and E. Tourís Gromov hyperbolicity through decomposition of metric spaces II J. Geom. Anal. 14 2004 123 149
23. J.M. Rodríguez, J.M. Sigarreta, J.-M. Vilaire, and M. Villeta On the hyperbolicity constant in graphs Discrete Math. 311 2011 211 219
24. J.M. Rodríguez, and E. Tourís Gromov hyperbolicity through decomposition of metric spaces Acta Math. Hungar. 103 2004 53 84
25. J.M. Rodríguez, and E. Tourís A new characterization of Gromov hyperbolicity for Riemann surfaces Publ. Mat. 50 2006 249 278
26. J.M. Rodríguez, and E. Tourís Gromov hyperbolicity of Riemann surfaces Acta Math. Sinica 23 2007 209 228
27. J.M. Sigarreta, Hyperbolicity in median graphs, Proc. Indian Acad. Sci. Math. Sci. 2013 (in press).
28. E. Tourís Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces J. Math. Anal. Appl. 380 2011 865 881
29. Y. Wu, and C. Zhang Hyperbolicity and chordality of a graph Electron. J. Combin. 18 2011 P43