Hyperbolicity and chordality of a graph.
Wu, Yaokun, Zhang, Chengpeng (2011)
The Electronic Journal of Combinatorics [electronic only]
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Wu, Yaokun, Zhang, Chengpeng (2011)
The Electronic Journal of Combinatorics [electronic only]
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José M. Rodríguez, José M. Sigarreta (2017)
Open Mathematics
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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 δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. Deciding whether or not a graph is hyperbolic is usually very difficult; therefore, it is interesting to find classes of graphs which are hyperbolic. A graph...
Biggs, Norman (1998)
The Electronic Journal of Combinatorics [electronic only]
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Alicia Cantón, Ana Granados, Domingo Pestana, José Rodríguez (2013)
Open Mathematics
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We 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 conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given....
T. McKee (1988)
Fundamenta Mathematicae
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Ryszard Szwarc (2003)
Colloquium Mathematicae
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Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from...
Ján Plesník (1977)
Mathematica Slovaca
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I.B. Lackovic, D.M. Cvetkovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Cvetkovic, Dragos M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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M. Kano, Changwoo Lee, Kazuhiro Suzuki (2008)
Discussiones Mathematicae Graph Theory
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For a set S of connected graphs, a spanning subgraph F of a graph is called an S-factor if every component of F is isomorphic to a member of S. It was recently shown that every 2-connected cubic graph has a {Cₙ | n ≥ 4}-factor and a {Pₙ | n ≥ 6}-factor, where Cₙ and Pₙ denote the cycle and the path of order n, respectively (Kawarabayashi et al., J. Graph Theory, Vol. 39 (2002) 188-193). In this paper, we show that every connected cubic bipartite graph has a {Cₙ | n ≥ 6}-factor, and has...
Jerzy Topp (1990)
Mathematica Slovaca
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