On the Hyperbolicity Constant in Graph Minors Articles uri icon

publication date

  • April 2018

international standard serial number (ISSN)

  • 1735-8515

abstract

  • 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.

keywords

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