Erdős, Paul; Hajnal, András Chromatic number of finite and infinite graphs and hypergraphs. (English) Zbl 0566.05029 Discrete Math. 53, 281-285 (1985). 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 Cited in 2 ReviewsCited in 7 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05C35 Extremal problems in graph theory 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics Keywords:uncountable chromatic number; bipartite graph; edge density; finite graphs; finite hypergraphs; infinite hypergraphs; infinite graphs PDFBibTeX XMLCite \textit{P. Erdős} and \textit{A. Hajnal}, Discrete Math. 53, 281--285 (1985; Zbl 0566.05029) Full Text: DOI 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 [6] Erdös, P.; Hajnal, A.; Szemerědi, E., On almost bipartite large chromatic graphs, Ann. Discrete Math., XII, 117-123 (1982), (See also for further results V. Rödl, Nearly bipartite graphs) · Zbl 0501.05033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.