Erdős Problem #1175

Let $\kappa$ be an uncountable cardinal. Must there exist a cardinal $\lambda$ such that every graph with chromatic number $\lambda$ contains a triangle-free subgraph with chromatic number $\kappa$?

#1175: [Va99,7.92]

set theory | chromatic number

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Shelah proved that a negative answer is consistent if $\kappa=\lambda=\aleph_1$.

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