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Asymptotic Analysis of Generating Functions Arising from Dynamic Graphs

Authors Nadja Azzouz , Olivier Bodini , Francis Durand , Bernhard Gittenberger

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LIPIcs.AofA.2026.30.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph enumeration
  • Mathematics of computing → Generating functions
Keywords
  • combinatorial enumeration
  • generating functions

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Abstract

We study generating functions arising from sequentially growing labeled graphs where at each step either a new vertex is created or a new edge between two existing vertices is added. We provide explicit representations of the generating functions and derive asymptotic formulas for their coefficients using Laplace’s method and Bessel function approximations in the undirected model, and Hayman admissibility combined with the saddle point method in the directed model. Finally, we study a natural parameter of each model and indicate further parameter studies.

Cite As Get BibTex

Nadja Azzouz, Olivier Bodini, Francis Durand, and Bernhard Gittenberger. Asymptotic Analysis of Generating Functions Arising from Dynamic Graphs. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AofA.2026.30

Author Details

Nadja Azzouz
  • Institute of Discrete Mathematics and Geometry, TU Wien, Austria
Olivier Bodini
  • Institut Galilée, Univ. Paris Nord, France
Francis Durand
  • Institut Galilée, Univ. Paris Nord, France
Bernhard Gittenberger
  • Institute of Discrete Mathematics and Geometry, TU Wien, Austria

Funding

  • Azzouz, Nadja: supported by the Austrian Science Foundation FWF, grant I-6744-N.
  • Bodini, Olivier: supported by the Agence Nationale de Recherche, grant ANR-23-CE48-0014
  • Durand, Francis: supported by the Agence Nationale de Recherche, grant ANR-23-CE48-0014
  • Gittenberger, Bernhard: supported by the Austrian Science Foundation FWF, grant I-6744-N.

References

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