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The k-Cut Model in Conditioned Galton-Watson Trees

Authors Gabriel Berzunza , Xing Shi Cai , Cecilia Holmgren



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Author Details

Gabriel Berzunza
  • Department of Mathematics, Uppsala University, Sweden
Xing Shi Cai
  • Department of Mathematics, Uppsala University, Sweden
Cecilia Holmgren
  • Department of Mathematics, Uppsala University, Sweden

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Gabriel Berzunza, Xing Shi Cai, and Cecilia Holmgren. The k-Cut Model in Conditioned Galton-Watson Trees. 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. 5:1-5:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.AofA.2020.5

Abstract

The k-cut number of rooted graphs was introduced by Cai et al. [Cai and Holmgren, 2019] as a generalization of the classical cutting model by Meir and Moon [Meir and Moon, 1970]. In this paper, we show that all moments of the k-cut number of conditioned Galton-Watson trees converge after proper rescaling, which implies convergence in distribution to the same limit law regardless of the offspring distribution of the trees. This extends the result of Janson [Janson, 2006].

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • k-cut
  • cutting
  • conditioned Galton-Watson trees

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References

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