Claims

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2002_12_04_komjath_shelah: Komjáth and Shelah (J. Graph Theory 2005) prove it consistent with ZFC that for every increasing f some graph of chromatic number aleph one has every n-chromatic subgraph on at least f(n) vertices; a yes answer is unprovable.

2019_02_21_lambie_hanson: Lambie-Hanson's theorem that for every function f there is a graph of chromatic number aleph_1 whose subgraphs of chromatic number k >= 3 all have at least f(k) vertices, answering the question no in ZFC; refereed in 2020.

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