31 citations · 104 across the 14 of their papers we have counts for
9 papers · 1 filter
Maximum degree in minor-closed classes of graphs
Omer Gimenez, Dieter Mitsche, Marc Noy
Given a class of graphs G closed under taking minors, we study the maximum degree Δ_n of random graphs from G with n vertices. We prove several lower and upper bounds that hold wit…
The maximum degree of planar graphs I. Series-parallel graphs
Michael Drmota, Omer Gimenez, Marc Noy
We prove that the maximum degree of a random series-parallel graph with vertices satisfies in probability, and for a c…
Asymptotic enumeration and limit laws for graphs of fixed genus
Guillaume Chapuy, Eric Fusy, Omer Gimenez +2
It is shown that the number of labelled graphs with n vertices that can be embedded in the orientable surface S_g of genus g grows asymptotically like …
Degree distribution in random planar graphs
Michael Drmota, Omer Gimenez, Marc Noy
We prove that for each , the probability that a root vertex in a random planar graph has degree tends to a computable constant , so that the expected number of vert…
Graph classes with given 3-connected components: asymptotic enumeration and random graphs
Omer Gimenez, Marc Noy, Juanjo Rue
Consider a family of 3-connected graphs of moderate growth, and let be the class of graphs whose 3-connected components are graphs in . We…
On the number of graphs not containing as a minor
S. Gerke, O. Gimenez, M. Noy +1
We derive precise asymptotic estimates for the number of labelled graphs not containing as a minor, and also for those which are edge maximal. Additionally, we establish…
Enumeration and limit laws of series-parallel graphs
Manuel Bodirsky, Omer Gimenez, Mihyun Kang +1
We show that the number of labelled series-parallel graphs on vertices is asymptotically , where and are explicit computable cons…
Asymptotic enumeration and limit laws of planar graphs
Omer Gimenez, Marc Noy
We show an asymptotic estimate for the number of labelled planar graphs on vertices. We also find limit laws for the number of edges, the number of connected components, and ot…
Multi-Path Matroids
Joseph E. Bonin, Omer Gimenez
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…