Israel Journal of Mathematics

, Volume 61, Issue 3, pp 285–294

Consistency results on infinite graphs

Authors

  • Péter Komjáth
    • Department of MathematicsLehigh University
    • Department of Computer ScienceEötvös University
Article

DOI: 10.1007/BF02772573

Cite this article as:
Komjáth, P. Israel J. Math. (1988) 61: 285. doi:10.1007/BF02772573

Abstract

Consistently there exist ℵ2-chromatic graphs with no ℵ1-chromatic subgraphs. The statement that every uncountably chromatic graph of size ℵ1 contains an uncountably chromaticω-connected subgraph is consistent and independent. It is consistent that there is an uncountably chromatic graph of size ℵω1 in which every subgraph with size less than ℵω1 is countably chromatic.

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© Hebrew University 1988