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**Zentralblatt MATH**

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

**Zbl.No: ** 573.05021

**Autor: ** Erdös, Paul

**Title: ** Problems and results on chromatic numbers in finite and infinite graphs. (In English)

**Source: ** Graph theory with applications to algorithms and computer science, Proc. 5th Int. Conf., Kalamazoo/Mich. 1984, 201-213 (1985).

**Review: ** [For the entire collection see Zbl 564.00004.]

In this paper some old and recent problems and results on chromatic numbers in finite and infinite graphs are discussed. For example: Let G be n-chromatic and the smallest odd circuit of which is 2k+1. Is it then true that the number of vertices of G is greater than n^{ck}, where c_{k} tends to infinity together with k? (Hajnal, Sauer and Erdös). Other authors of the problems and results quoted in this paper are El-Zahar, Baumgartner, Laver, Foreman, Shelah, Taylor, Galvin, Komjath, Rödl, Rothschild, Graham, Fan Chung, Simonovits, Toft, Dirac, Folkman, Nesetril, Szemerédi, and Lovász.

**Reviewer: ** I.Tomescu

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

05-02 Research monographs (combinatorics)

00A07 Problem books

**Keywords: ** chromatic number; product of graphs; infinite chromatic number; generalized continuum hypothesis; edge critical graph

**Citations: ** Zbl 564.00004

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