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 nck, where ck 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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