Results 1 to 10 of about 101 (88)
Gromov hyperbolicity of planar graphs
Open Mathematics, 2013 AbstractWe prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this ...
Domingo de Guzman Pestana +1 more
exaly +4 more sources
Worm Domains are not Gromov Hyperbolic. [PDF]
J Geom Anal, 2023 AbstractWe show that Worm domains are not Gromov hyperbolic with respect to the Kobayashi distance.
Arosio L, Dall'Ara GM, Fiacchi M.
europepmc +7 more sources
Gromov Hyperbolicity in Directed Graphs [PDF]
Symmetry, 2020 In this paper, we generalize the classical definition of Gromov hyperbolicity to the context of directed graphs and we extend one of the main results of the theory: the equivalence of the Gromov hyperbolicity and the geodesic stability. This theorem has potential applications to the development of solutions for secure data transfer on the internet.
Ana Portilla +2 more
exaly +4 more sources
Gromov hyperbolic cubic graphs [PDF]
Open Mathematics, 2012 If X is a geodesic metric space and $x_1,x_2,x_3\in X$, a geodesic triangle $T=\{x_1,x_2,x_3\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\delta$-hyperbolic $($in the Gromov sense$)$ if any side of $T$ is contained in a $\delta$-neighborhood of the union of the two other sides, for every ...
Pestana Domingo +3 more
doaj +5 more sources
On Computing the Gromov Hyperbolicity [PDF]
Journal of Experimental Algorithmics, 2015 The Gromov hyperbolicity is an important parameter for analyzing complex networks which expresses how the metric structure of a network looks like a tree. It is for instance used to provide bounds on the expected stretch of greedy-routing algorithms in Internet-like graphs.
David Coudert
exaly +3 more sources
Gromov Hyperbolicity of Riemann Surfaces [PDF]
Acta Mathematica Sinica, English Series, 2006 In this paper we study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its "building block components". We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it.
Eva Touris Lojo, José M Rodríguez
exaly +4 more sources
Gromov Hyperbolicity in Mycielskian Graphs [PDF]
Symmetry, 2017 Since the characterization of Gromov hyperbolic graphs seems a too ambitious task, there are many papers studying the hyperbolicity of several classes of graphs. In this paper, it is proven that every Mycielskian graph G M is hyperbolic and that δ ( G M ) is comparable to diam ( G M ) .
Ana Portilla +2 more
exaly +4 more sources
Bounds on Gromov hyperbolicity constant [PDF]
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2015 If $X$ is a geodesic metric space and $x_{1},x_{2},x_{3} \in X$, a geodesic triangle $T=\{x_{1},x_{2},x_{3}\}$ is the union of the three geodesics $[x_{1}x_{2}]$, $[x_{2}x_{3}]$ and $[x_{3}x_{1}]$ in $X$. The space $X$ is $δ$-hyperbolic in the Gromov sense if any side of $T$ is contained in a $δ$-neighborhood of the union of the two other sides, for ...
Domingo de Guzman Pestana +1 more
exaly +4 more sources
Geometric characterizations of Gromov hyperbolicity [PDF]
Inventiones Mathematicae, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zoltan Balogh, Stephen M Buckley
exaly +3 more sources
Knot graphs and Gromov hyperbolicity [PDF]
Mathematische Zeitschrift, 2022 We define a broad class of graphs that generalize the Gordian graph of knots. These knot graphs take into account unknotting operations, the concordance relation, and equivalence relations generated by knot invariants. We prove that overwhelmingly, the knot graphs are not Gromov hyperbolic, with the exception of a particular family of quotient knot ...
Stanislav Jabuka +2 more
openaire +3 more sources