6 citations · 7 across the 5 of their papers we have counts for
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math.CO2024
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…
math.CO2019★ 6 cited
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…
math.CO2014★ 1 cited
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…