Degree distribution in random planar graphs (2009)
Drmota, Michael, Gimenez, Omer, Noy, Marc
We prove that for each $k\ge0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, so that the expected number of vertices of degree $k$...
Graph classes with given 3-connected components: asymptotic enumeration and random graphs (2009)
Gimenez, Omer, Noy, Marc, Rue, Juanjo
Consider a family $\mathcal{T}$ of 3-connected graphs of moderate growth, and let $\mathcal{G}$ be the class of graphs whose 3-connected components are graphs in $\mathcal{T}$. We present a general...
We present a domain-independent algorithm that computes macros in a novel way. Our algorithm computes macros "on-the-fly" for a given set of states and does not require previously learned or inferred...
Enumeration and limit laws of series-parallel graphs (2005)
Bodirsky, Manuel, Gimenez, Omer, Kang, Mihyun, Noy, Marc
We show that the number $g_n$ of labelled series-parallel graphs on $n$ vertices is asymptotically $g_n \sim g\cdot n^{-5/2} \gamma^n n!$, where $\gamma$ and $g$ are explicit computable constants. We...
Asymptotic enumeration and limit laws of planar graphs (2005)
We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in...
Bonin, Joseph E., Gimenez, Omer
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis...