923.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 923

References:

erdosproblems.com/923
[Er69b] Erdős, P., Problems and results in chromatic graph theory. Proof Techniques in Graph Theory (1969), 27-35.
[Ro77] Rödl, V., On the chromatic number of subgraphs of a given graph. Proc. Amer. Math. Soc. (1977), 370-371.

Imports (1)

FormalConjecturesUtil

theorem Erdos923.erdos_923 Is it true that, for every $k$, there is some $f(k)$ such that if $G$ has chromatic number $\geq f(k)$ then $G$ contains a triangle-free subgraph with chromatic number $\geq k$? sorry line 42 source
Source documentation
Is it true that, for every $k$, there is some $f(k)$ such that if $G$ has chromatic number $\geq f(k)$ then $G$ contains a triangle-free subgraph with chromatic number $\geq k$?
This is true, as shown by Rödl [Ro77].

depends on sorry what this means
Statement uses: Iff, True, Nat, Exists, SimpleGraph, LE.le, ENat, SimpleGraph.chromaticNumber, And, SimpleGraph.CliqueFree, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_923 : answer(True) ↔ ∀ (V : Type*) (n : ℕ),
    ∃ k : ℕ, ∀ G : SimpleGraph V, k ≤ G.chromaticNumber →
    ∃ H ≤ G, n ≤ H.chromaticNumber ∧ H.CliqueFree 3 := by
…
```