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The k-cut number of rooted graphs was introduced by Cai et al. [7] as a generalization of the classical cutting model by Meir and Moon [16]. 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 [13]. 2012 ACM Subject Classification Mathematics of computing → Probabilistic algorithms

The k-Cut Model in Conditioned Galton-Watson Trees.