Large induced trees in sparse random graphs
โ Scribed by A.M Frieze; B Jackson
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 621 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0095-8956
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๐ SIMILAR VOLUMES
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
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
## Abstract For a graph __G__, let __a__(__G__) denote the maximum size of a subset of vertices that induces a forest. Suppose that __G__ is connected with __n__ vertices, __e__ edges, and maximum degree ฮ. Our results include: (a) if ฮโโคโ3, and __G__โโ โ__K__~4~, then __a__(__G__)โโฅโ__n__โโโe/4โโโ1
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