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declared open (Lean) · formalized · $500erdos:146
If HH is bipartite and rr-degenerate, is ex(n;H)≪n2−1/r\mathrm{ex}(n;H) \ll n^{2-1/r} (a $500 Erdős-Simonovits prize conjecture)? A counterexample refutes the degeneracy conjecture.
graph theoryturan numberN/A3 sources
declared open (Lean) · formalizederdos:180
For every finite family F\mathcal{F} of graphs, is there a single G∈FG \in \mathcal{F} with ex(n;G)≪Fex(n;F)\mathrm{ex}(n;G) \ll_{\mathcal{F}} \mathrm{ex}(n;\mathcal{F})? A counterexample refutes the Erdős-Simonovits compactness conjecture.
graph theoryturan numberN/A4 sources
declared open · formalizederdos:579
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.indepNum
graph theoryturan numberN/A2 sources
declared disproved (Lean) · formalizederdos:794
False ↔ ∀ (n : ℕ) (H : Finset (Finset (Fin (3 * n)))), H.IsThreeUniform → n ^ 3 + 1 ≤ H.card → H.ContainsSubgraph 4 3 ∨ H.ContainsSubgraph 5 7
graph theoryhypergraphsturan numberN/A5 sources

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