6 citations · 7 across the 5 of their papers we have counts for
5 papers
Asymptotic expansion of regular and connected regular graphs
Élie de Panafieu
We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergue…
The Erdős-Rényi Random Graph Conditioned on Every Component Being a Clique
Martijn Gösgens, Lukas Lüchtrath, Elena Magnanini +2
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can…
Limit Distribution of Two Skellam Distributions, Conditionally on Their Equality
François Durand, Élie de Panafieu
Consider two random variables following Skellam distributions of parameters going to infinity linearly. We prove that the limit distribution of the first variable, conditionally on…
Symbolic method and directed graph enumeration
Élie de Panafieu, Sergey Dovgal
We introduce the arrow product, a systematic generating function technique for directed graph enumeration. It provides short proofs for previous results of Gessel on the number of…
Limit law for number of components of fixed sizes of graphs with degree one or two
Nicolas Broutin, Élie de Panafieu
We consider graphs with vertices of degree 1 or 2 and prove that the numbers of components of sizes 2 to q have a limit normal distribution for any q > 1. The result is also extend…