منابع مشابه
The shape of unlabeled rooted random trees
Abstract. We consider the number of nodes in the levels of unlabelled rooted random trees and show that the stochastic process given by the properly scaled level sizes weakly converges to the local time of a standard Brownian excursion. Furthermore we compute the average and the distribution of the height of such trees. These results extend existing results for conditioned Galton-Watson trees a...
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For arbitrary positive integers h and m, we consider the family of all rooted trees of height h having exactly m vertices at distance h from the root. We refer to such trees as (h,m)-trees. For a tree T from this family, we consider a simple random walk on T which starts at the root and terminates when it visits one of the m vertices at distance h from the root. Consider the problem of finding ...
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A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.
متن کاملk-Protected Vertices in Unlabeled Rooted Plane Trees
We find a simple, closed formula for the proportion of vertices which are k -protected in all unlabeled rooted plane trees on n vertices. We also find that, as n goes to infinity, the average rank of a random vertex in a tree of size n approaches 0.727649, and the average rank of the root of a tree of size n approaches 1.62297. Mathematics Subject Classification 05A15 · 05A16 · 05C05 tree, enum...
متن کاملDiverse families of Random rooted trees A compilation of characteristics
This diploma thesis deals with four big groups of random trees, namely Polya trees, simple generated trees, increasing trees and scale-free trees. Di erent characteristics, similarities and di erences of these varieties are discussed, e.g. the limiting distribution of node-degrees. Most results are obtained using generating functions and methods of singulary analysis and stochastics. In the rst...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2010.05.011