833.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 833

References:

erdosproblems.com/833
[ErLo75] Erdős, P. and Lovász, L., Problems and results on {$3$}-chromatic hypergraphs and some related questions. (1975), 609--627.

Imports (1)

FormalConjecturesUtil

theorem Erdos833.erdos_833 Does there exist an absolute constant sorry line 43 source
Source documentation
Does there exist an absolute constant $c>0$ such that, for all $r\geq 2$, in any $r$-uniform hypergraph with chromatic number $3$ there is a vertex contained in at least $(1+c)^r$ many edges?
This was solved by Erdős and Lovász [ErLo75], who proved in particular that there is a vertex contained in at least $\frac{2^{r-1}}{4r}$ many edges.

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, LT.lt, OfNat.ofNat, Nat, LE.le, Finset, Fin, Finset.IsUniform, Finset.HasHypergraphChromaticNumber, HPow.hPow, HAdd.hAdd, Finset.hypergraphDegree
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
34 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_833 :
    answer(True) ↔ ∃ c : ℝ, 0 < c ∧ ∀ r : ℕ, 2 ≤ r →
    ∀ (n : ℕ) (H : Finset (Finset (Fin n))),
      H.IsUniform r → H.HasHypergraphChromaticNumber 3 →
        ∃ v : Fin n, (1 + c) ^ r ≤ (H.hypergraphDegree v : ℝ) := by
…
```
Mentions: c