Combinatorics
A Lean-verified submission was approved for this target. Read the recorded review for its precise mathematical scope.
Submitted by Jordan
erdos_579.variants.ehss_large_delta), and the
difficulty is to push the edge-density threshold down to an arbitrary .
Here is the complete tripartite graph with all parts of size , encoded as
completeMultipartiteGraph (fun _ : Fin 3 => Fin 2); "contains no " is expressed
via SimpleGraph.Free.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«579»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos579.erdos_579" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (δ : ℝ),
0 < δ →
∃ c,
0 < c ∧
∀ᶠ (n : ℕ) in Filter.atTop,
∀ (G : SimpleGraph (Fin n)),
Erdos579.octahedron.Free G → δ * ↑n ^ 2 ≤ ↑G.edgeFinset.card → c * ↑n ≤ ↑G.indepNumOriginal conjecture source: FormalConjectures/ErdosProblems/579.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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Individual lemmas, special cases and supporting work, shown in their original scope.
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