Erdős problem 533 · problems.science

Let $\delta > 0$ . If $n$ is sufficiently large and $G$ is a graph on $n$ vertices with no $K_5$ and at least $\delta n^2$ edges, must $G$ contain a set of $\gg_\delta n$ vertices spanning no triangle?

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FormalConjectures/ErdosProblems/533.lean

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FormalConjectures/ErdosProblems/533.leanErdos533.erdos_5338 linesExact file

1False ↔2  ∀ (δ : ℝ),3    0 < δ →4      ∃ c,5        0 < c ∧6          ∀ᶠ (n : ℕ) in Filter.atTop,7            ∀ (G : SimpleGraph (Fin n)),8              G.CliqueFree 5 → δ * ↑n ^ 2 ≤ ↑G.edgeFinset.card → ∃ S, c * ↑n ≤ ↑S.card ∧ G.CliqueFreeOn (↑S) 3

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