# Consistency results on infinite graphs

Article

- Received:

DOI: 10.1007/BF02772573

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

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## Abstract

Consistently there exist ℵ_{2}-chromatic graphs with no ℵ_{1}-chromatic subgraphs. The statement that every uncountably chromatic graph of size ℵ_{1} contains an uncountably chromatic*ω*-connected subgraph is consistent and independent. It is consistent that there is an uncountably chromatic graph of size ℵ_{ω}_{1} in which every subgraph with size less than ℵ_{ω}_{1} is countably chromatic.

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© Hebrew University 1988