Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  586.05024
Autor:  Erdös, Paul; Erné, Marcel
Title:  Clique numbers of graphs. (In English)
Source:  Discrete Math. 59, 235-242 (1986).
Review:  Author's abstract: "For each natural number n, let G(n) be the set of all numbers c such that there exists a graph of order n and with exactly c cliques, where the empty set is also considered to be a clique. The authors verify the asymptotic approximation |G(n)| = 0(2n· n-2/5) and show that every integer between n+1 and 2n-6n^{5/6} belongs to G(n). They thenconclude that limn ––> oo\frac{|G(n)|}{2n} = 0, while limn ––> oo\frac{|G(n)|}{an} = oo for all a with 0 < a < 2."
Reviewer:  O.Oellermann
Classif.:  * 05C35 Extremal problems (graph theory)
                   05C99 Graph theory
Keywords:  cliques; asymptotic approximation

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