The $k$-Cut Model in Deterministic and Random Trees

The \(k\)-cut number of rooted graphs was introduced by Cai et al. as a generalization the classical cutting model Meir and Moon. In this paper, we show that all moments conditioned Galton-Watson trees converge after proper rescaling, which implies convergence in distribution to same limit law regardless offspring trees. This extends result Janson. Using method, also various random or deterministic logarithmic height converges probability constant such split-trees, uniform recursive trees, scale-free