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Local Central Limit Theorems for Subgraph Counts in Subcritical Graph Families

Authors Michael Drmota , Yitian Wang

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LIPIcs.AofA.2026.6.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
  • Mathematics of computing → Discrete mathematics
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Generating functions
  • Mathematics of computing → Probability and statistics
Keywords
  • Subcritical graph classes
  • subgraph counts
  • generating functions
  • functional equations

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Abstract

It was already established in [Drmota et al., 2017] that subgraph counts in vertex labelled subcritial graph families satisfy a central limit theorem. This result is now sharpened to local central limit theorems. Furthermore this result is generalized to unlabelled subcritical graph families and to multivariate central limit theorems for the joint distribution of finitely many subgraph counts.

Cite As Get BibTex

Michael Drmota and Yitian Wang. Local Central Limit Theorems for Subgraph Counts in Subcritical Graph Families. 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. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AofA.2026.6

Author Details

Michael Drmota
  • TU Wien, Institute of Discrete Mathematics and Geometry, Austria
Yitian Wang
  • TU Wien, Institute of Discrete Mathematics and Geometry, Austria

Funding

  • Drmota, Michael: This work was partially supported by the Austrian Science Fund FWF, projects P 35016, 10.55776/F1002.
  • Wang, Yitian: This work was supported by the Austrian Science Fund FWF, project 10.55776/F1002.

References

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