Next Article in Journal
Testing Lorentz Symmetry Using High Energy Astrophysics Observations
Next Article in Special Issue
β-Differential of a Graph
Previous Article in Journal
A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory
Previous Article in Special Issue
Gromov Hyperbolicity in Mycielskian Graphs
Open AccessArticle

Generalized Chordality, Vertex Separators and Hyperbolicity on Graphs

Department of Economic analysis and Finances, Universidad de Castilla-La Mancha, Avda. Real Fábrica de Sedas s/n, 45600 Talavera de la Reina, Spain
Symmetry 2017, 9(10), 199; https://doi.org/10.3390/sym9100199
Received: 21 August 2017 / Revised: 18 September 2017 / Accepted: 19 September 2017 / Published: 24 September 2017
(This article belongs to the Special Issue Graph Theory)
A graph is chordal if every induced cycle has exactly three edges. A vertex separator set in a graph is a set of vertices that disconnects two vertices. A graph is δ -hyperbolic if every geodesic triangle is δ -thin. In this paper, we study the relation between vertex separator sets, certain chordality properties that generalize being chordal and the hyperbolicity of the graph. We also give a characterization of being quasi-isometric to a tree in terms of chordality and prove that this condition also characterizes being hyperbolic, when restricted to triangles, and having stable geodesics, when restricted to bigons. View Full-Text
Keywords: infinite graph; geodesic; Gromov hyperbolic; chordal; bottleneck property; vertex separator. infinite graph; geodesic; Gromov hyperbolic; chordal; bottleneck property; vertex separator.
Show Figures

Figure 1

MDPI and ACS Style

Martínez-Pérez, Á. Generalized Chordality, Vertex Separators and Hyperbolicity on Graphs. Symmetry 2017, 9, 199.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop