Analytic combinatorics of connected graphs
Combinatorics
2018-10-12 v3 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1605.08597,
title = {Analytic combinatorics of connected graphs},
author = {Elie de Panafieu},
journal= {arXiv preprint arXiv:1605.08597},
year = {2018}
}
Comments
38 pages + 22 pages of appendix, long version of the talk arXiv:1604.07307 accepted at FPSAC 2016