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Open AccessArticle

Mathematical Properties on the Hyperbolicity of Interval Graphs

1
Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 54, La Garita, Acapulco 39650, Mexico
2
Department of Mathematics, Carlos III University of Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(11), 255; https://doi.org/10.3390/sym9110255
Received: 3 October 2017 / Revised: 21 October 2017 / Accepted: 27 October 2017 / Published: 1 November 2017
(This article belongs to the Special Issue Graph Theory)
Gromov hyperbolicity is an interesting geometric property, and so it is natural to study it in the context of geometric graphs. In particular, we are interested in interval and indifference graphs, which are important classes of intersection and Euclidean graphs, respectively. Interval graphs (with a very weak hypothesis) and indifference graphs are hyperbolic. In this paper, we give a sharp bound for their hyperbolicity constants. The main result in this paper is the study of the hyperbolicity constant of every interval graph with edges of length 1. Moreover, we obtain sharp estimates for the hyperbolicity constant of the complement of any interval graph with edges of length 1. View Full-Text
Keywords: interval graphs; indifference graphs; euclidean graphs; geometric graphs; Gromov hyperbolicity; geodesics interval graphs; indifference graphs; euclidean graphs; geometric graphs; Gromov hyperbolicity; geodesics
MDPI and ACS Style

Hernández-Gómez, J.C.; Reyes, R.; Rodríguez, J.M.; Sigarreta, J.M. Mathematical Properties on the Hyperbolicity of Interval Graphs. Symmetry 2017, 9, 255.

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