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Chromatic number of finite and infinite graphs and hypergraphs. (English) Zbl 0566.05029

In this survey the authors state some old and new solved and unsolved problems concerning the chromatic number of finite and infinite graphs and hypergraphs, raised by Galvin, Shelah, Komlós, Komjath, Mihoc, Burr, Szemerédi, Nešetřil, Rödl, Taylor and the authors.
Reviewer: I.Tomescu

MSC:

05C15 Coloring of graphs and hypergraphs
05C35 Extremal problems in graph theory
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
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References:

[1] Erdös, P., Graph theory and probability I and II, Canad. Math. J., 11, 346-352 (1961) · Zbl 0097.39102
[2] Erdös, P.; Hajnal, A., On chromatic number of graphs and set systems, Acta Math. Acad. Sci. Hungar, 17, 61-99 (1966) · Zbl 0151.33701
[3] Erdös, P.; Hajnal, A., On chromatic number of infinite graphs, (Proc. Coll. Tihany (1966)), 83-89, see also
[4] Ajtai; Komlos, J.; Szemerědi, E., A note on Ramsey numbers, J. Combin. Theory A, 29, 354-360 (1980), [4] · Zbl 0455.05045
[5] Hajnal, A.; Komjath, P., What must and what need not be contained in a graph of uncountable chromatic number, Combinatorica, 4, 47-52 (1984), for many further results, see · Zbl 0541.05026
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