### authors

- Carballosa, Walter
- RODRIGUEZ GARCIA, JOSE MANUEL
- Rosario, Omar
- Sigarreta, Jose M

- Overview

- April 2018

- 1735-8515

- A graph H is a minor of a graph G if a graph isomorphic to H can be obtained from G by contracting some edges, deleting some edges, and deleting some isolated vertices. The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. One of the main aims in this work is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph G/e obtained from the (simple or non-simple) graph G by contracting an arbitrary edge e from it. We prove that H is hyperbolic if and only if G is hyperbolic, for many minors H of G, even if H is obtained from G by contracting and/or deleting infinitely many edges.

- Graph minor; Edge contraction; Deleted edge; Hyperbolic graph; Geodesics

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Universidad Carlos III de Madrid
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