منابع مشابه
Hyperbolicity and Chordality of a Graph
Let G be a connected graph with the usual shortest-path metric d. The graph G is δ-hyperbolic provided for any vertices x, y, u, v in it, the two larger of the three sums d(u, v) + d(x, y), d(u, x) + d(v, y) and d(u, y) + d(v, x) differ by at most 2δ. The graph G is k-chordal provided it has no induced cycle of length greater than k. Brinkmann, Koolen and Moulton find that every 3-chordal graph...
متن کاملSemi-hyperbolicity and Hyperbolicity
We prove that for C1-diffeomorfisms semi-hyperbolicity of an invariant set implies its hyperbolicity. Moreover, we provide some exact estimations of hyperbolicity constants by semi-hyperbolicity ones, which can be useful in strict numerical computations.
متن کاملDistortion of the Hyperbolicity Constant of a Graph
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δneighborhood of the union of the other two sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) ...
متن کاملWhen Can Graph Hyperbolicity Be Computed in Linear Time?
Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known practical algorithms for computing the hyperbolicity number of a n-vertex graph have running time O(n). Exploiting the framework of parameterized comp...
متن کاملNotes on Hyperbolicity Cones
minimize cx such that Ax = b and x ∈ Λ+, where c ∈ R, Ax = b is a system of linear equations and Λ+ is the closure of a so called hyperbolicity cone. Hyperbolic programming generalizes semidefinite programming, but it is not known to what extent since it is not known how general the hyperbolicity cones are. The rich algebraic structure of hyperbolicity cones makes hyperbolic programming an inte...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2018
ISSN: 2073-8994
DOI: 10.3390/sym10090360