Hajnal, A.; Komjáth, P. Some remarks on the simultaneous chromatic number. (English) Zbl 1048.03039 Combinatorica 23, No. 1, 89-104 (2003). The authors present partial results, variants and consistency results concerning a yet unsolved conjecture. The conjecture is due to P. Erdős, F. Galvin and A. Hajnal [in: A. Hajnal et al. (eds.), Infinite and finite sets, Colloq. Math. Soc. János Bolyai 10, 425–513 (1975; Zbl 0324.04005)] and says that if \(X\) is a graph on the ground set \(V\) with \(\chi(X)=\aleph_1\), then \(X\) has an edge coloring \(F\) with \(\aleph_1\) colors such that if \(V\) is decomposed into \(\aleph_0\) parts then there is one part in which \(F\) takes all values. Reviewer: András Pluhár (Szeged) Cited in 2 Documents MSC: 03E35 Consistency and independence results 05C15 Coloring of graphs and hypergraphs Keywords:edge colorings; infinite graphs; consistency Citations:Zbl 0324.04005 PDFBibTeX XMLCite \textit{A. Hajnal} and \textit{P. Komjáth}, Combinatorica 23, No. 1, 89--104 (2003; Zbl 1048.03039) Full Text: DOI