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arXiv · 1605.08597

Analytic combinatorics of connected graphs

Elie de Panafieu
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Abstract

We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie generating function manipulations, we derive a formula for the coefficients of the complete asymptotic expansion. The same result is derived for connected multigraphs.

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Elie de Panafieu. 2018-10-11. Analytic combinatorics of connected graphs. https://arxiv.org/abs/1605.08597

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