Hyperbolicity and complement of graphs

Applied Mathematics Letters

Volumn 24, Issue 11, 2011, Pages 1882-1887

  Bermudo, Sergio ^a   Rodríguez, José M ^b   Sigarreta, José M ^c   Tourís, Eva ^b  

^a UNIVERSIDAD PABLO DE OLAVIDE   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^c UNIVERSIDAD AUTÓNOMA DE GUERRERO   (Mexico)

Author keywords

Complement; Connectivity; Geodesic; Graph; Gromov hyperbolicity

Indexed keywords

COMPLEMENT; CONNECTIVITY; GEODESIC; GRAPH; HYPERBOLICITY;

SET THEORY; TOPOLOGY;

GEODESY;

EID: 79959775188     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2011.05.011     Document Type: Article

References (18)

1. S. Bermudo, J.M. Rodríguez, J.M. Sigarreta, and J.-M. Vilaire Mathematical properties of Gromov hyperbolic graphs AIP Conf. Proc. 281 2010 575 578
2. S. Bermudo, J.M. Rodríguez, J.M. Sigarreta, J.-M. Vilaire, Gromov hyperbolic graphs (submitted for publication).
3. G. Brinkmann, J. Koolen, and V. Moulton On the hyperbolicity of chordal graphs Ann. Comb. 5 2001 61 69
4. 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.
5. E.A. Jonckheere Contrle du trafic sur les réseaux géometrie hyperboliqueUne approche mathématique a la sécurité de l'acheminement de l'information J. Eur. Syst. Autom. 37 2 2003 145 159
6. E.A. Jonckheere, P. Lohsoonthorn, Geometry of network security, in: American Control Conference ACC, 2004, pp. 111151.
7. J.H. Koolen, and V. Moulton Hyperbolic bridged graphs European J. Combin. 23 2002 683 699 (Pubitemid 39659438)
8. J. Michel, J.M. Rodríguez, J.M. Sigarreta, M. Villeta, Hyperbolicity and parameters of graphs, Ars Combin. (in press).
9. J. Michel, J.M. Rodríguez, J.M. Sigarreta, M. Villeta, Gromov hyperbolicity in Cartesian product graphs, Proc. Indian Acad. Sci. Math. Sci. (in press).
10. A. Portilla, J.M. Rodríguez, and E. Tourís Gromov hyperbolicity through decomposition of metric spaces II J. Geom. Anal. 14 2004 123 149
11. J.M. Rodríguez, J.M. Sigarreta, J.-M. Vilaire, and M. Villeta On the hyperbolicity constant in graphs Discrete Math. 311 2011 211 219
12. J.M. Rodríguez, and E. Tourís Gromov hyperbolicity of Riemann surfaces Acta Math. Sinica 23 2007 209 228
13. K. Oshika Discrete Groups 2002 AMS Bookstore
14. P.A. Hst, H. Lindén, A. Portilla, J.M. Rodríguez, E. Tourís, Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics, J. Math. Soc. Japan (in press).
15. P.A. Hst, A. Portilla, J.M. Rodríguez, and E. Tourís Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains Bull. Lond. Math. Soc. 42 2 2010 282 294
16. P.A. Hst, A. Portilla, J.M. Rodríguez, E. Tourís, Uniformly separated sets and Gromov hyperbolicity of domains with the quasihyperbolic metric, Medit. J. Math. in press (doi:10.1007/s00009-010-0059-7 ).
17. A. Portilla, and E. Tourís A characterization of Gromov hyperbolicity of surfaces with variable negative curvature Publ. Mat. 53 2009 83 110
18. E. Ghys, and P. de la Harpe Sur les Groupes Hyperboliques d'aprs Mikhael Gromov Progress in Mathematics vol. 83 1990 Birkhuser Boston Inc. Boston, MA