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Erdős problem 740

Let m\mathfrak{m} be an infinite cardinal and GG be a graph with chromatic number m\mathfrak{m}. Let r≥1r\geq 1. Must GG contain a subgraph of chromatic number m\mathfrak{m} which does not contain any odd cycle of length ≤r\leq r?

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FormalConjectures/ErdosProblems/

740.lean

Retained formal statement1 of 1

Let m\mathfrak{m} be an infinite cardinal and GG be a graph with chromatic number m\mathfrak{m}. Let r≥1r\geq 1. Must GG contain a subgraph of chromatic number m\mathfrak{m} which does not contain any odd cycle of length ≤r\leq r?

FormalConjectures/ErdosProblems/740.leanErdos740.erdos_7404 linesExact file
True ↔  ∀ (V : Type u_1) (G : SimpleGraph V),    Cardinal.aleph0 ≤ G.chromaticCardinal →      ∀ (r : ℕ), ∃ H, H.coe.chromaticCardinal = G.chromaticCardinal ∧ Erdos740.NoShortOddCycle H.coe r
OpenStatement only, no proof

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