Resumen de Graphs with small hyperbolicity constant and hyperbolic minor graphs

Omar Rosario Cayetano

• The structure of this work is as follows.

  Chapter 1 is an introduction to graph theory. In Chapter 2 we give a brief introduction to hyperbolic spaces in the Gromov sense and we consider some previous results regarding hyperbolicity.

  In Chapter 3, Section 3.1 we study the properties of graphs with small hyperbolicity constants, i.e., the graphs which are like trees (in the Gromov sense). In Section 3.2 we give a partial answer to the question: What is the structure of graphs with small hyperbolicity constant? The answer relates the hyperbolicity constant to the effective diameter.

  Finally, in Chapter 4 we obtain quantitative information about the distortion of the hyperbolicity constant of the graph Gn e (respectively, G=e ) obtained from the graph G by deleting (respectively, contracting) an arbitrary edge e from it.