Erdős problem 595 · problems.science

Erdős Problem 595 (250): Is there an infinite graph G which contains no $K_4$ and is not the union of countably many triangle-free graphs?

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7 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

595.lean

Retained formal statement7 of 7

Triangle-free graphs are trivially countable unions of triangle-free graphs: if G is already triangle-free, then G = ⨆ i : ℕ, G_i where G_0 = G and G_i = ⊥ for i ≥ 1.

FormalConjectures/ErdosProblems/595.leanErdos595.erdos_595.variants.triangle_free_is_union1 lineExact file

1∀ {V : Type u_1} (G : SimpleGraph V), G.CliqueFree 3 → Erdos595.IsCountableUnionOfTriangleFree G

TextbookStatement only, no proof

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