Study of the Gromov hyperbolicity constant on graphs

The concept of Gromov hyperbolicity grasps the essence of negatively curved spaces like the classical hyperbolic space and Riemannian manifolds of negative sectional curvature. It is remarkable that a simple concept leads to such a rich general theory. The study of hyperbolic graphs is an interesting topic since the hyperbolicity of any geodesic metric space is equivalent to the hyperbolicity of a graph related to it. In this Ph. D. Thesis we characterize the hyperbolicity constant of interval graphs and circular-arc graphs. Likewise, we provide relationships between dominant sets and the hyperbolicity constant. Finally, we study the invariance of the hyperbolicity constant when the graphs are transformed by several operators.Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Domingo de Guzmán Pestana Galván.- Secretaria: Ana Portilla Ferreira.- Vocal: Eva Tourís Loj

On several extremal problems in graph theory involving gromov hyperbolicity constant

Mención Internacional en el título de doctorIn this Thesis we study the extremal problems of maximazing and minimazing the hyperbolicity constant on several families of graphs. In order to properly raise our research problem, we need to introduce some important definitions and make some remarks on the graphs we study.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Elena Romera Colmenarejo.- Secretario: Ana María Portilla Ferreira.- Vocal: José María Sigarreta Almir