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erdos_1067

Specification

Does every graph with chromatic number $\aleph_1$ contain an infinitely connected subgraph with chromatic number $\aleph_1$? Komjáth [Ko13] proved that it is consistent that the answer is no. This was improved by Soukup [So15], who constructed a counterexample using no extra set-theoretical assumptions. A simpler elementary example was given by Bowler and Pitz [BoPi24].

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Lean 4 Statement 
theorem erdos_1067 :
    answer(False) ↔ ∀ (V : Type) (G : SimpleGraph V), G.chromaticCardinal = ℵ_ 1 →
      ∃ (H : G.Subgraph), H.coe.chromaticCardinal = ℵ_ 1 ∧ InfinitelyConnected H.coe
ID: ErdosProblems__1067__erdos_1067
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