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Problems · Vela Mathematics Program

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6 problemsGraph view
declared open · formalizederdos:60
∃ c > 0, ∀ᶠ (n : ℕ) in Filter.atTop, ∀ (G : SimpleGraph (Fin n)) [inst : DecidableRel G.Adj], SimpleGraph.extremalNumber n (SimpleGraph.cycleGraph 4) < G.edgeFinset.card → c * √↑n ≤ ↑{H' | Nonempty (H'.coe ≃g SimpleGraph.cycleGraph 4)}.ncard
graph theorycyclesA0068552 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 proved (Lean) · formalizederdos:71
True ↔ ∀ (P : Set ℕ), P.IsAPOfLength ⊤ → (∃ n ∈ P, Even n) → ∃ c, ∀ (V : Type) [inst : Fintype V] [DecidableEq V] (G : SimpleGraph V) [inst_2 : DecidableRel G.Adj], c ≤ G.averageDegree → ∃ v w, w.IsCycle ∧ w.length ∈ P
graph theorycyclesN/A4 sources
declared open · formalized · $500erdos:74
∀ {V : Type u} {G : SimpleGraph V} (A : G.Subgraph), (Erdos74.SimpleGraph.edgeDistancesToBipartite A).Nonempty
graph theorychromatic numbercyclesN/A2 sources
declared open · formalizederdos:108
True ↔ ∀ r ≥ 4, ∀ k ≥ 2, ∃ f, ∀ (V : Type u) (G : SimpleGraph V), Nonempty V → ↑f ≤ G.chromaticNumber → ∃ H, H.coe.girth ≥ r ∧ H.coe.chromaticNumber ≥ ↑k
graph theorychromatic numbercyclespossible2 sources
declared open · formalizederdos:184
∃ f, (f =O[Filter.atTop] fun n => ↑n) ∧ ∀ {V : Type u_1} [inst : Fintype V] [DecidableEq V] (G : SimpleGraph V), ∃ D, (∀ H ∈ D, Erdos184.IsCycleOrEdge H.coe) ∧ Erdos184.IsDecomposition G D ∧ ↑D.card ≤ f (Fintype.card V)
graph theorycyclespossible2 sources