Claims

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1967_01_01_erdos_hajnal: For every c below one half, a graph of chromatic number aleph-0 whose every finite induced subgraph on m vertices has an independent set of size at least cm; this settles Problem 750 for every f(m) = epsilon m.

1982_01_01_erdos_hajnal_szemeredi: For every epsilon and every cardinal kappa, a graph of chromatic number above kappa whose every finite n-vertex subgraph becomes bipartite after deleting epsilon n vertices; this covers Problem 750 for f(m) = epsilon m.

2026_05_03_chojecki: A graph of infinite chromatic number whose every m-vertex finite subgraph becomes bipartite after deleting at most g(m) vertices, for any unbounded nondecreasing g; this answers Problem 750 yes.

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