159.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 159

References:

erdosproblems.com/159
[Er78] Erdős, P., Problems and results in combinatorial analysis and combinatorial number theory. Proc. Ninth Southeastern Conf. Combinatorics, Graph Theory and Computing (1978), 29-40.
[Sp77] Spencer, J., Asymptotic lower bounds for Ramsey functions. Discrete Math. (1977), 69-76.

Imports (1)

FormalConjecturesUtil

theorem Erdos159.erdos_159 There exists some constant $c>0$ such that $$R(C_4,K_n) \ll n^{2-c}.$$ The prize of $100 is offered in [Er78] for a proof or disproof sorry line 43 source
Source documentation
There exists some constant $c>0$ such that $$R(C_4,K_n) \ll n^{2-c}.$$
The prize of $100 is offered in [Er78] for a proof or disproof.
This problem is #17 in Ramsey Theory in the graphs problem collection.

depends on sorry what this means
Statement uses: Exists, Real, LT.lt, OfNat.ofNat, Nat, LE.le, SimpleGraph.graphRamsey, Fin, SimpleGraph.cycleGraph, SimpleGraph.completeGraph, HMul.hMul, HPow.hPow, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
36 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_159 :
    ∃ (c : ℝ) (_ : 0 < c) (C : ℝ),
      ∀ (n : ℕ), 1 ≤ n →
        (SimpleGraph.graphRamsey (SimpleGraph.cycleGraph 4)
          (SimpleGraph.completeGraph (Fin n)) : ℝ) ≤ C * (n : ℝ) ^ (2 - c) := by
…
```
Mentions: c, SimpleGraph.graphRamsey