GraphConjecture4.lean`

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Written on the Wall II - Conjecture 4

Reference: E. DeLaVina, Written on the Wall II, Conjectures of Graffiti.pc

Imports (1)

FormalConjecturesUtil

theorem WrittenOnTheWallII.GraphConjecture4.conjecture4 Documented declaration: conjecture4 sorry line 44 source
Source documentation
WOWII Conjecture 4
If G is a connected graph then the maximum number of leaves over all spanning trees satisfies Ls(G) ≥ NG(G) - 1 where NG(G) is the minimal neighbourhood size of a non-edge of G.

L4DEL explanation
WOWII Conjecture 4 If G is a connected graph then the maximum number of leaves over all spanning trees satisfies Ls(G) ≥ NG(G) - 1 where NG(G) is the minimal neighbourhood size of a non-edge of G.
Sources and attribution: Pinned Lean source (1646ca16afd6)

depends on sorry what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, DecidableRel, SimpleGraph.Adj, Nontrivial, SimpleGraph.Connected, LE.le, Real, HSub.hSub, SimpleGraph.NG, OfNat.ofNat, SimpleGraph.Ls
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Nat
11 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture4 (G : SimpleGraph α) [DecidableRel G.Adj] [Nontrivial α] (h_conn : G.Connected) :
    NG G - 1 ≤ Ls G := by
…
```