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Local Central Limit Theorems for Subgraph Counts in Subcritical Graph Families

Authors: Michael Drmota and Yitian Wang

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)


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.

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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)


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@InProceedings{drmota_et_al:LIPIcs.AofA.2026.6,
  author =	{Drmota, Michael and Wang, Yitian},
  title =	{{Local Central Limit Theorems for Subgraph Counts in Subcritical Graph Families}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.6},
  URN =		{urn:nbn:de:0030-drops-262779},
  doi =		{10.4230/LIPIcs.AofA.2026.6},
  annote =	{Keywords: Subcritical graph classes, subgraph counts, generating functions, functional equations}
}
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