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Fringe Trees for Random Trees with Given Vertex Degrees

Authors Gabriel Berzunza Ojeda, Cecilia Holmgren, Svante Janson

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Author Details

Gabriel Berzunza Ojeda
  • Department of Mathematical Sciences, University of Liverpool, UK
Cecilia Holmgren
  • Department of Mathematics, Uppsala University, Sweden
Svante Janson
  • Department of Mathematics, Uppsala University, Sweden

Funding

  • Holmgren, Cecilia: Supported by the Knut and Alice Wallenberg Foundation; Ragnar Söderberg’s Foundation; the Swedish Research Council.
  • Janson, Svante: Supported by the Knut and Alice Wallenberg Foundation; the Swedish Research Council.

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Gabriel Berzunza Ojeda, Cecilia Holmgren, and Svante Janson. Fringe Trees for Random Trees with Given Vertex Degrees. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.AofA.2024.1

Abstract

We prove that the number of fringe subtrees, isomorphic to a given tree, in uniformly random trees with given vertex degrees, asymptotically follows a normal distribution. As an application, we establish the same asymptotic normality for random simply generated trees (conditioned Galton-Watson trees). Our approach relies on an extension of Gao and Wormald’s (2004) theorem to the multivariate setting.

Subject Classification

ACM Subject Classification
  • Mathematics of computing
Keywords
  • Conditioned Galton-Watson trees
  • fringe trees
  • simply generated trees
  • uniformly random trees with given vertex degrees

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