Erdős problem 1067 · problems.science

Does every graph with chromatic number $\aleph_1$ contain an infinitely connected subgraph with chromatic number $\aleph_1$ ?

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FormalConjectures/ErdosProblems/

1067.lean

Retained formal statement2 of 2

Thomassen [Th17] constructed a counterexample to the version which asks for infinite edge-connectivity (that is, to disconnect the graph requires deleting infinitely many edges).

FormalConjectures/ErdosProblems/1067.leanErdos1067.erdos_1067.variants.infinite_edge_connectivity4 linesExact file

1False ↔2  ∀ (V : Type) (G : SimpleGraph V),3    G.chromaticCardinal = Cardinal.aleph 1 →4      ∃ H, H.coe.chromaticCardinal = Cardinal.aleph 1 ∧ Erdos1067.InfinitelyEdgeConnected H.coe

SolvedStatement only, no proof

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