##
**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(2^{n}· n^{-2/5}) and show that every integer between n+1 and 2^{n-6n^{5/6}} belongs to G(n). They thenconclude that **lim**_{n ––> oo}\frac{|G(n)|}{2^{n}} = 0, while **lim**_{n ––> oo}\frac{|G(n)|}{a^{n}} = oo for all a with 0 < a < 2."

**Reviewer: ** O.Oellermann

**Classif.: ** * 05C35 Extremal problems (graph theory)

05C99 Graph theory

**Keywords: ** cliques; asymptotic approximation

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag