A study of the orders of maximal induced trees in a random graph G, with small edge probability p is given. In particular, it is shown that the giant component of almost every G,, where p = c/n and c > 1 is a constant, contains only very small maximal trees (that are of a specific type) and very lar
Induced trees in sparse random graphs
โ Scribed by W. Fernandez de la Vega
- Publisher
- Springer Japan
- Year
- 1986
- Tongue
- English
- Weight
- 278 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The author proved that, for c > 1, the random graph G(n, p ) on n vertices with edge probability p = c / n contains almost always an induced tree on at least q n ( 1 -o( 1)) vertices, where L Y ~ is the positive root of the equation CLY = log( 1 + c'a). It is shown here that if c is sufficiently lar
The performance of the greedy coloring algorithm ''first fit'' on sparse random graphs G and on random trees is investigated. In each case, approximately n, c r n log log n colors are used, the exact number being concentrated almost surely on at 2 most two consecutive integers for a sparse random gr