Let T n denote the set of unrooted unlabeled trees of size n and let k โฅ 1 be given. By assuming that every tree of T n is equally likely, it is shown that the limiting distribution of the number of nodes of degree k is normal with mean value โผ ยต k n and variance โผ ฯ 2 k n with positive constants ยต
On the altitude of specified nodes in random trees
โ Scribed by Helmut Prodinger
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 130 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let T be a plane rooted tree with n nodes which is regarded as family tree of a Galton-Watson branching process conditioned on the total progeny. The profile of the tree ' may be described by the number of nodes or the number of leaves in layer t n , respectively. It is shown that these two processe
Multidimensional binary trees represent a symbiosis of trees and tries, and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d-dimensional binary tree can be partitioned into layers according to the nodes appearing in the ith dimension. We d
Denote by \(S_{n}\) the set of all distinct rooted binary trees with \(n\) unlabeled vertices. Define \(\sigma_{n}\) as a total height of a tree chosen at random in the set \(S_{n}\), assuming that all the possible choices are equally probable. The total height of a tree is defined as the sum of the
We determine the asymptotic behavior of the expected value and the variance of the log-product of the subtree-sizes of trees T belonging to simply generated families of n
## Abstract We analyze a fringe tree parameter w in a variety of settings, utilizing a variety of methods from the analysis of algorithms and data structures. Given a tree __t__ and one of its leaves __a__, the w(__t,โa__) parameter denotes the number of internal nodes in the subtree rooted at __a