1035.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 1035

References:

erdosproblems.com/1035
[Er93] Erdős, Paul, Some of my favorite solved and unsolved problems in graph theory. Quaestiones Math. (1993), 333-350.

Imports (1)

FormalConjecturesUtil

theorem Erdos1035.erdos_1035 Is there a constant $c > 0$ such that every graph on $2^n$ vertices with minimum degree $> (1-c) \cdot 2^n$ contains the $n$-dimensional hypercube $Q_n$? sorry line 42 source
Source documentation
Is there a constant $c > 0$ such that every graph on $2^n$ vertices with minimum degree $> (1-c) \cdot 2^n$ contains the $n$-dimensional hypercube $Q_n$?
This is Erdős's question [Er93, p. 345].
See also [576] for the extremal number of edges that guarantee a $Q_n$.

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, GT.gt, OfNat.ofNat, Nat, SimpleGraph, Fin, HPow.hPow, DecidableRel, SimpleGraph.Adj, SimpleGraph.degree, Membership.mem, Set, SimpleGraph.neighborSet, HMul.hMul, HSub.hSub, SimpleGraph.IsContained and 2 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
48 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1035 : answer(sorry) ↔
    ∃ c > 0, ∀ n : ℕ, ∀ (G : SimpleGraph (Fin (2 ^ n))) [DecidableRel G.Adj],
      (∀ v, (G.degree v : ℝ) > (1 - c) * 2 ^ n) →
        (SimpleGraph.hypercube n).IsContained G := by
…
```
Mentions: c, SimpleGraph.hypercube