Erdős problem 1067

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

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

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