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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 794.05086

**Autor: ** Erdös, Paul; Hattingh, Johannes H.

**Title: ** Asymptotic bounds for irredundant Ramsey numbers. (In English)

**Source: ** Quaest. Math. 16, No.3, 319-331 (1993).

**Review: ** Let G(V,E) be a graph. A set of vertices X\subseteq V is said to be irredundant if each vertex x in X is either an isolated vertex in the subgraph induced by X or there is vertex y in V-X which is incident with x and no other vertex in X. The irredundant Ramsey number s(m,n) is the smallest positive integer s so that, in every red-blue coloring of the edges of the complete graph on s vertices, either the blue graph contains an m-element irredundant set or the red graph contains an n-element irredundant set. The main result of this paper is

Theorem 1. For each m \geq 3 there is a positive constant C_{m} such that s(m,n) > C_{m}**(**{n\over log n}**)**^{{m2- m-1\over 2(m-1)}}.

**Reviewer: ** J.E.Graver (Syracuse)

**Classif.: ** * 05C55 Generalized Ramsey theory

**Keywords: ** bounds; irredundant Ramsey number

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag