On the independence number of random graphs
β Scribed by A.M. Frieze
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 239 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Let (Y(G~,~) denote the independence number of the random graph Gn,p. Let d = np. We show that if E > 0 is fixed then with probability going to 1 as n + m cu(G& -$t (log d -log log dlog 2 + 1) < 7 provided d, s d = o(n), where d, is some fixed constant.
π SIMILAR VOLUMES
Caro (1979) and Wei (1981) established a bound on the size of an independent set of a graph as a function of its degrees. In case the degrees of each vertex's neighbors are also known, we establish a lower bound which is tighter for most graphs.
In this paper we use the degree sequence, order, size and vertex connectivity of a K 1,,+ 1 -free graph or of an almost claw-free graph to obtain several upper bounds on its independence number. We also discuss the sharpness of these results.