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**Zentralblatt MATH**

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

**Zbl.No: ** 591.05030

**Autor: ** Erdös, Paul; Füredi, Z.; Hajnal, András; Komjáth, P.; Rödl, Vojtech; Seress, Á.

**Title: ** Coloring graphs with locally few colors. (In English)

**Source: ** Discrete Math. 59, 21-34 (1986).

**Review: ** Authors' abstract: "Let G be a graph, m > r \geq 1 integers. Suppose that it has a good coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r- colorings. One of our results (Theorem 2.4) states: The chromatic number of G, Chr(G) \leq r2^{r} log_{2} log_{2} m and this value is the best possible in a certain sense. We consider infinite graphs as well."

**Reviewer: ** I.Tomescu

**Classif.: ** * 05C15 Chromatic theory of graphs and maps

**Keywords: ** strong limit cardinal; intersecting Sperner family; local r-colorings; chromatic number; infinite graphs

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