108.lean`

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L4DEL: Lean4 Domain Explanation Language

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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 108

Reference: erdosproblems.com/108

Imports (1)

FormalConjecturesUtil

theorem Erdos108.erdos_108 For every r ≥ 4 and k ≥ 2 is there some finite f(k,r) such that every graph of chromatic number ≥ f(k,r) contains a subgraph of girth ≥ r and chromatic number ≥ k? sorry line 39 source
Source documentation
For every r ≥ 4 and k ≥ 2 is there some finite f(k,r) such that every graph of chromatic number ≥ f(k,r) contains a subgraph of girth ≥ r and chromatic number ≥ k?

depends on sorry what this means
Statement uses: Iff, True, Nat, GE.ge, OfNat.ofNat, Exists, SimpleGraph, Nonempty, LE.le, ENat, SimpleGraph.chromaticNumber, SimpleGraph.Subgraph, And, SimpleGraph.girth, SimpleGraph.Subgraph.verts, SimpleGraph.Subgraph.coe
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_108 :
    answer(sorry) ↔ ∀ r ≥ 4, ∀ k ≥ (2 : ℕ), ∃ (f : ℕ),
    ∀ (V : Type u) (G : SimpleGraph V) (_ : Nonempty V)
      (hchro : f ≤ SimpleGraph.chromaticNumber G),
    ∃ (H : G.Subgraph), (SimpleGraph.girth H.coe ≥ r) ∧
    (SimpleGraph.chromaticNumber H.coe ≥ k) := by
…
```