𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Asymptotic Normality of the Vertex Degree in Random Subgraphs of the n-Cube

✍ Scribed by Urszula Konieczna

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
245 KB
Volume
154
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

We consider two types of random subgraphs of the n-cube. For these models we study the asymptotic behaviour of the number of vertices of degree d.

πŸ“œ SIMILAR VOLUMES

The Distribution of the Maximum Vertex D
The Distribution of the Maximum Vertex Degree in Random Planar Maps
✍ Zhicheng Gao; Nicholas C. Wormald πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 297 KB

We determine the limiting distribution of the maximum vertex degree 2 n in a random triangulation of an n-gon, and show that it is the same as that of the maximum of n independent identically distributed random variables G 2 , where G 2 is the sum of two independent geometric(1Γ‚2) random variables.

On the asymptotic distributions of subgr
On the asymptotic distributions of subgraph counts in a random tournament
✍ Pontus Andersson πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 191 KB πŸ‘ 2 views

A random tournament T is obtained by independently orienting the edges of n 1 the complete graph on n vertices, with probability for each direction. We study the 2 asymptotic distribution, as n tends to infinity, of a suitable normalization of the number of subgraphs of T that are isomorphic to a gi

The distribution of nodes of given degre
The distribution of nodes of given degree in random trees
✍ Drmota, Michael; Gittenberger, Bernhard πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 391 KB πŸ‘ 2 views

Let T n denote the set of unrooted unlabeled trees of size n and let k β‰₯ 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 ∼ Β΅ k n and variance ∼ Οƒ 2 k n with positive constants Β΅

The asymptotic distribution of long cycl
The asymptotic distribution of long cycles in random regular graphs
✍ Hans Garmo πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 580 KB

The asymptotic distribution of the number of cycles of length l in a random r-regular graph is determined. The length of the cycles is defined as a function of the Ε½ . Ε½ . number of vertices n, thus l s l n , and the length satisfies l n Βͺ Ο± as n Βͺ Ο±. The limiting Ε½ . Ε½ . distribution turns out to