Abstract:
All graphs we consider in this talk are lablled. The enumeration of planar graphs was obtained in 2005 by Giménez and Noy. Shortly after, Bodirsky et al. solved in 2007 the problem of counting cubic (3-regular) planar graphs. Recently we have revisited their work and extended some of their results. Also, we have been able to solve the problem of counting of 4-regular planar graphs, which is considerably harder. In the talk we will review these problems and the common combinatorial, algebraic and analytic techniques used in their solution. In all cases we compute the associated exponential generating functions and derive from them precise asymptotic estimates. This is joint work with Clément Requilé and Juanjo Rué.