Counting connected graphs with large excess

We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations, we derive the complete asymptotic expansion.

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Vydáno v:	Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autor:	De Panafieu, Élie
Médium:	Journal Article Konferenční příspěvek
Jazyk:	angličtina
Vydáno:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Témata:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics Combinatorics
ISSN:	1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí:	We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations, we derive the complete asymptotic expansion.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6368