منابع مشابه
The cut-tree of large recursive trees
Imagine a graph which is progressively destroyed by cutting its edges one after the other in a uniform random order. The so-called cut-tree records key steps of this destruction process. It can be viewed as a random metric space equipped with a natural probability mass. In this work, we show that the cut-tree of a random recursive tree of size n, rescaled by the factor n−1 lnn, converges in pro...
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If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.
متن کاملThe cut-tree of large galton-watson trees and the brownian crt
Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton-Watson tree with finite variance and conditioned...
متن کاملThe Subtree Size Profile of Bucket Recursive Trees
Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial...
متن کاملBranches in random recursive k-ary trees
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2015
ISSN: 0246-0203
DOI: 10.1214/13-aihp597