Distortion of the hyperbolicity constant in minor graphs

The main aim in this work is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph G\e (respectively, G/e) obtained from the graph G by deleting (respectively, contracting) an arbitrary edge e from it. 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. Since we deal with connected graphs, our work provides information about the hyperbolicity constant of minor graphs.