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A note on the independence number, domination number and related parameters of random binary search trees and random recursive trees
Michael Fuchs, Cecilia Holmgren, Dieter Mitsche +1
We identify the mean growth of the independence number of random binary search trees and random recursive trees and show normal fluctuations around their means. Similarly we also s…
The -cut model in deterministic and random trees
Gabriel Berzunza, Xing Shi Cai, Cecilia Holmgren
The -cut number of rooted graphs was introduced by Cai et al. as a generalization of the classical cutting model by Meir and Moon. In this paper, we show that all moments of the…
Cutting resilient networks -- complete binary trees
Xing Shi Cai, Cecilia Holmgren
In our previous work, we introduced the random -cut number for rooted graphs. In this paper, we show that the distribution of the -cut number in complete binary trees of size…
K-cut on paths and some trees
Xing Shi Cai, Luc Devroye, Cecilia Holmgren +1
We define the (random) -cut number of a rooted graph to model the difficulty of the destruction of a resilient network. The process is as the cut model of Meir and Moon except n…
Multivariate normal limit laws for the numbers of fringe subtrees in -ary search trees and preferential attachment trees
Cecilia Holmgren, Svante Janson, Matas Šileikis
We study fringe subtrees of random -ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that…
Bootstrap percolation on Galton-Watson trees
Béla Bollobás, Karen Gunderson, Cecilia Holmgren +2
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number , the -neighbou…