547.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 547

References:

erdosproblems.com/547
[Bu74] Burr, S. A., Generalized Ramsey theory for graphs—a survey. Graphs and combinatorics (Proc. Capital Conf., George Washington Univ., Washington, D.C., 1973) (1974), 52-75.
[Zh11] Zhao, Y., Proof of the $(n/2-n/2-n/2)$ conjecture for large $n$. Electron. J. Combin. (2011), Paper 27, 61.

Imports (1)

FormalConjecturesUtil

theorem Erdos547.erdos_547 If $T$ is a tree on $n$ vertices then $$R(T) \leq 2n-2.$$ This problem is #14 in Ramsey Theory in the graphs problem collection sorry line 44 source
Source documentation
If $T$ is a tree on $n$ vertices then $$R(T) \leq 2n-2.$$
This problem is #14 in Ramsey Theory in the graphs problem collection.

depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, SimpleGraph, Fin, SimpleGraph.IsTree, SimpleGraph.diagonalGraphRamsey, HSub.hSub, HMul.hMul
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
14 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_547 :
    ∀ (n : ℕ) (hn : 2 ≤ n) (T : SimpleGraph (Fin n)),
      T.IsTree → SimpleGraph.diagonalGraphRamsey T ≤ 2 * n - 2 := by
…
```
Mentions: SimpleGraph.diagonalGraphRamsey
theorem Erdos547.erdos_547.variants.sufficiently_large For sufficiently large $n$, every tree $T$ on $n$ vertices satisfies $R(T)\leq 2n-2$ sorry line 54 source
Source documentation
For sufficiently large $n$, every tree $T$ on $n$ vertices satisfies $R(T)\leq 2n-2$. Proved by Zhao [Zh11].

depends on sorry what this means
Statement uses: Filter.Eventually, Nat, SimpleGraph, Fin, SimpleGraph.IsTree, LE.le, SimpleGraph.diagonalGraphRamsey, HSub.hSub, HMul.hMul, OfNat.ofNat, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_547.variants.sufficiently_large :
    ∀ᶠ n : ℕ in atTop, ∀ T : SimpleGraph (Fin n),
      T.IsTree → SimpleGraph.diagonalGraphRamsey T ≤ 2 * n - 2 := by
…
```
Mentions: SimpleGraph.diagonalGraphRamsey