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Block Statistics in Subcritical Graph Classes

Authors Dimbinaina Ralaivaosaona, Clément Requilé, Stephan Wagner

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Author Details

Dimbinaina Ralaivaosaona
  • Stellenbosch University, South Africa
Clément Requilé
  • Technische Universität Wien, Austria
Stephan Wagner
  • Uppsala University, Sweden
  • Stellenbosch University, South Africa

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Dimbinaina Ralaivaosaona, Clément Requilé, and Stephan Wagner. Block Statistics in Subcritical Graph Classes. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 24:1-24:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


We study block statistics in subcritical graph classes; these are statistics that can be defined as the sum of a certain weight function over all blocks. Examples include the number of edges, the number of blocks, and the logarithm of the number of spanning trees. The main result of this paper is a central limit theorem for statistics of this kind under fairly mild technical assumptions.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Random graphs
  • Mathematics of computing → Generating functions
  • subcritical graph class
  • block statistic
  • number of blocks
  • number of edges
  • number of spanning trees


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