A central limit theorem for decomposable random variables with applications to random graphs
Journal of Combinatorial Theory Series B
Average-case analysis of algorithms and data structures
Handbook of theoretical computer science (vol. A)
Poisson approximations for functionals of random trees
Proceedings of the seventh international conference on Random structures and algorithms
On convergence rates in the central limit theorems for combinatorial structures
European Journal of Combinatorics
CAAP '92 Proceedings of the 17th Colloquium on Trees in Algebra and Programming
Asymptotic degree distribution in random recursive trees
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Level of nodes in increasing trees revisited
Random Structures & Algorithms
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In this work we study edge weights for two specific families of increasing trees, which include binary increasing trees and plane-oriented recursive trees as special instances, where plane-oriented recursive trees serve as a combinatorial model of scale-free random trees given by the m = 1 case of the Barabási–Albert model. An edge e = (k, l), connecting the nodes labelled k and l, respectively, in an increasing tree, is associated with the weight we = |k − l|. We are interested in the distribution of the number of edges with a fixed edge weight j in a random generalized plane-oriented recursive tree or random d-ary increasing tree. We provide exact formulas for expectation and variance and prove a normal limit law for this quantity. A combinatorial approach is also presented and applied to a related parameter, the maximum edge weight.