Erdős problem 108
For every r ≥ 4 and k ≥ 2 is there some finite f(k,r) such that every graph of chromatic number ≥ f(k,r) contains a subgraph of girth ≥ r and chromatic number ≥ k?
Sources
FormalConjectures/ErdosProblems/
108.lean
Retained formal statement
For every r ≥ 4 and k ≥ 2 is there some finite f(k,r) such that every graph of chromatic number ≥ f(k,r) contains a subgraph of girth ≥ r and chromatic number ≥ k?
True ↔ ∀ r ≥ 4, ∀ k ≥ 2, ∃ f, ∀ (V : Type u) (G : SimpleGraph V), Nonempty V → ↑f ≤ G.chromaticNumber → ∃ H, H.coe.girth ≥ r ∧ H.coe.chromaticNumber ≥ ↑kOpenStatement only, no proof