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declared falsifiable · formalizederdos:23
∀ (n : ℕ), 0 < n → ∀ H ≤ Erdos23.blowupC5 n, H.IsBipartite → n ^ 2 ≤ ((Erdos23.blowupC5 n).edgeFinset \ H.edgeFinset).card
graph theoryA3896462 sources
declared falsifiable · formalized · $1000erdos:64
True ↔ ∀ (V : Type u_1) (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj], G.minDegree ≥ 3 → ∃ k v c, k ≥ 2 ∧ c.IsCycle ∧ c.length = 2 ^ k
graph theorycyclesN/A2 sources
declared falsifiable · formalized · $250erdos:128
True ↔ ∀ (V : Type) [inst : Fintype V] (G : SimpleGraph V), (∀ (V' : Set V), 2 * V'.ncard + 1 ≥ Fintype.card V → 50 * (SimpleGraph.induce V' G).edgeSet.ncard > Fintype.card V ^ 2) → ¬G.CliqueFree 3
graph theoryN/A2 sources
declared falsifiableerdos:167
Erdős problem 167
graph theoryN/A
declared falsifiableerdos:548
Erdős problem 548
graph theoryN/A
declared falsifiableerdos:583
Erdős problem 583
graph theoryN/A
declared falsifiable · formalizederdos:617
∀ r ≥ 3, ∀ {V : Type} [inst : Fintype V] [DecidableEq V], Fintype.card V = r ^ 2 + 1 → ∀ (coloring : Sym2 V → Fin r), ∃ S k, S.card = r + 1 ∧ ∀ u ∈ S, ∀ v ∈ S, u ≠ v → coloring s(u, v) ≠ k
graph theoryN/A2 sources
declared falsifiable · formalizederdos:628
∀ (V : Type u_1) [Fintype V] (G : SimpleGraph V) (k : ℕ), G.chromaticNumber = ↑k → G.CliqueFree k → ∀ (a b : ℕ), a ≥ 2 → b ≥ 2 → a + b = k + 1 → ∃ s, (SimpleGraph.induce s G).chromaticNumber ≥ ↑a ∧ (SimpleGraph.induce sᶜ G).chromaticNumber ≥ ↑b
graph theorychromatic numberN/A2 sources
declared falsifiableerdos:743
Erdős problem 743
graph theoryN/A2 sources
declared falsifiableerdos:993
Erdős problem 993
graph theoryA000055 · possible
declared falsifiableerdos:1020
Erdős problem 1020
graph theoryhypergraphsN/A
Vela Mathematics Program: problems · problems.science