Results 241 to 250 of about 83,569 (275)
Some of the next articles are maybe not open access.
SIAM Journal on Discrete Mathematics, 2003
Summary: The shortest-path metric \(d\) of a graph \(G=(V,E)\) is called \(\delta\)-hyperbolic if for any four vertices \(u,v,w,x\in X\) the two larger of the three sums \(d(u,v)+d(w,x)\), \(d(u,w)+d(v,x)\), \(d(u,x)+d(v,w)\) differ by at most \(\delta.\) In this paper, we characterize the graphs with 1-hyperbolic metrics in terms of a convexity ...
Bandelt, Hans-Jürgen, Chepoi, Victor
openaire +2 more sources
Summary: The shortest-path metric \(d\) of a graph \(G=(V,E)\) is called \(\delta\)-hyperbolic if for any four vertices \(u,v,w,x\in X\) the two larger of the three sums \(d(u,v)+d(w,x)\), \(d(u,w)+d(v,x)\), \(d(u,x)+d(v,w)\) differ by at most \(\delta.\) In this paper, we characterize the graphs with 1-hyperbolic metrics in terms of a convexity ...
Bandelt, Hans-Jürgen, Chepoi, Victor
openaire +2 more sources
Gromov Hyperbolicity of Periodic Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cantón, Alicia +3 more
openaire +1 more source
2023
This work proposes codebook encodings for graph networks that operate on hyperbolic manifolds. Where graph networks commonly learn node representations in Euclidean space, recent work has provided a generalization to Riemannian manifolds, with a particular focus on the hyperbolic space.
openaire +3 more sources
This work proposes codebook encodings for graph networks that operate on hyperbolic manifolds. Where graph networks commonly learn node representations in Euclidean space, recent work has provided a generalization to Riemannian manifolds, with a particular focus on the hyperbolic space.
openaire +3 more sources
Planarity and Hyperbolicity in Graphs
Graphs and Combinatorics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carballosa, Walter +3 more
openaire +1 more source
Cliques in Hyperbolic Random Graphs
Algorithmica, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Thomas Bläsius +2 more
openaire +1 more source
Scaled Gromov hyperbolic graphs
Journal of Graph Theory, 2007AbstractIn this article, the δ‐hyperbolic concept, originally developed for infinite graphs, is adapted to very large but finite graphs. Such graphs can indeed exhibit properties typical of negatively curved spaces, yet the traditional δ‐hyperbolic concept, which requires existence of an upper bound on the fatness δ of the geodesic triangles, is unable
Edmond Jonckheere +2 more
openaire +1 more source
On the Hyperbolicity of Chordal Graphs
Annals of Combinatorics, 2001The hyperbolicity of a metric space is the infimum of all \(\delta\) for which \(d(x,y)+ d(u,v)\leq \max\{d(x, u)+ d(y,v), d(x,v)+ d(y,u)\}+ \delta\) for all elements \(x\), \(y\), \(u\), \(v\) from the space. The notion can be viewed as expressing how `tree like' the space is, as spaces with hyperbolicity \(0\) are precisely the metric trees.
Brinkmann, Gunnar +2 more
openaire +2 more sources
The Hyperbolic Plane and Hyperbolic Graphs
2013The aim of this section is to give a very short introduction to planar hyperbolic geometry. Some good references for parts of this section are [CFKP97] and [ABC+91]. We first discuss the hyperbolic plane. Nets in the hyperbolic plane are concrete examples of the more general hyperbolic graphs. Hyperbolicity is reflected in the behaviour of random walks
openaire +1 more source
Hyperbolic Graph Efficiency Measures
1985In chapter 3 we developed a series of measures of the efficiency with which a production unit uses variable inputs to produce a given output vector. These measures are appropriate under a behavioral assumption of constrained cost minimization. In chapter 4 we developed an analogous series of measures of the efficiency with which a production unit ...
Rolf Färe +2 more
openaire +1 more source
Self-Avoiding Walks on Hyperbolic Graphs
Combinatorics, Probability and Computing, 2005We study self-avoiding walks (SAWs) on non-Euclidean lattices that correspond to regular tilings of the hyperbolic plane (‘hyperbolic graphs’). We prove that on all but at most eight such graphs, (i) there are exponentially fewer $N$-step self-avoiding polygons than there are $N$-step SAWs, (ii) the number of $N$-step SAWs grows as $\mu_w^N$ within a ...
Madras, Neal, Wu, C. Chris
openaire +2 more sources