Geodesic
Chordality properties and hyperbolicity on graphs
Álvaro Martínez-Pérez1
1Universidad de Castilla-La Mancha
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. In this paper we study the relation between the hyperbolicity of the graph and some chordality properties which are natural generalizations of being chordal. We find chordality properties that are weaker and stronger than being $\delta$-hyperbolic. Moreover, we obtain a characterization of being hyperbolic on terms of a chordality property on the triangles.
DOI : 10.37236/5315
Classification : 05C63, 05C10, 05C12
Mots-clés : infinite graph, geodesic, Gromov hyperbolic, chordal

Álvaro Martínez-Pérez  1

1 Universidad de Castilla-La Mancha 
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Álvaro Martínez-Pérez. Chordality properties and hyperbolicity on graphs. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5315

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