Juanjo Rué

Asymptotic Study of Subcritical Graph Classes

We present a unified general method for the asymptotic study of graphs from the so-called subcritical graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works in both the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number

A lower bound for the size of a minkowski sum of dilates

g_n/n!

Dynamic programming for graphs on surfaces

(resp.,

Asymptotic enumeration of non-crossing partitions on surfaces

g_n

Enumerating simplicial decompositions of surfaces with boundaries

) of labelled (resp., unlabelled) graphs on

Many 2-Level Polytopes from Matroids

n

Pentagonal chains and annuli as models for designing nanostructures from cages

vertices from a subcritical graph class

Subgraph statistics in subcritical graph classes

{\mathcal{G}}=\cup_n {\mathcal{G}_n}

On the sum of digits of some sequences of integers

satisfies asymptotically the universal behavior

On the limiting distribution of the metric dimension for random forests

g_n = c \!n^{-5/2} \!\gamma^n \! (1+o(1))