800.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 800

References:

erdosproblems.com/800
[Al94] Alon, N., Subdivided graphs have linear Ramsey numbers. J. Graph Theory (1994), 343-347.

Imports (1)

FormalConjecturesUtil

theorem Erdos800.erdos_800 If $G$ is a graph on $n$ vertices which has no two adjacent vertices of degree $\geq 3$ then $$R(G)\ll n,$$ where the implied constant is absolute sorry line 40 source
Source documentation
If $G$ is a graph on $n$ vertices which has no two adjacent vertices of degree $\geq 3$ then $$R(G)\ll n,$$ where the implied constant is absolute.
A problem of Burr and Erdős. Solved in the affirmative by Alon [Al94].

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, GT.gt, OfNat.ofNat, Nat, Fintype, SimpleGraph, DecidableRel, SimpleGraph.Adj, Eq, Fintype.card, Not, LE.le, SimpleGraph.degree, Membership.mem, Set, SimpleGraph.neighborSet and 2 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_800 : answer(True) ↔
    ∃ C > (0 : ℝ), ∀ (n : ℕ) (V : Type) [Fintype V] (G : SimpleGraph V) [DecidableRel G.Adj],
      Fintype.card V = n →
      (∀ u v, G.Adj u v → ¬(3 ≤ G.degree u ∧ 3 ≤ G.degree v)) →
      (SimpleGraph.diagonalGraphRamsey G : ℝ) ≤ C * n := by
…
```
Mentions: SimpleGraph.diagonalGraphRamsey