On the independence number of random graphs

Let α( G n,p ) denote the independence number of the random graph G n,p . Let d= np. We show that if ϵ > 0 is fixed then with probability going to 1 as n → ∞ ∥α(G n,p )– 2 n d (logd–loglogd–log2+1)∥⩽ ϵn d provided d ϵ ⩽ d= o( n), where d ϵ is some fixed constant.

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Bibliographic Details
Published in	Discrete mathematics Vol. 81; no. 2; pp. 171 - 175
Main Author	Frieze, A.M.
Format	Journal Article
Language	English
Published	Amsterdam Elsevier B.V 01.04.1990 Elsevier
Subjects	Combinatorics Combinatorics. Ordered structures Exact sciences and technology Graph theory Mathematics Sciences and techniques of general use Probability Graph theory Random graph Inequality
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Summary:	Let α( G n,p ) denote the independence number of the random graph G n,p . Let d= np. We show that if ϵ > 0 is fixed then with probability going to 1 as n → ∞ ∥α(G n,p )– 2 n d (logd–loglogd–log2+1)∥⩽ ϵn d provided d ϵ ⩽ d= o( n), where d ϵ is some fixed constant.
ISSN:	0012-365X 1872-681X
DOI:	10.1016/0012-365X(90)90149-C