GraphConjecture6.lean`

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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 6

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

Imports (1)

FormalConjecturesUtil

theorem WrittenOnTheWallII.GraphConjecture6.conjecture6 WOWII Conjecture 6 For a connected graph G we have Ls(G) ≥ 1 + n(G) - m(G) - a(G) where a(G) is defined via independent sets sorry line 42 source
Source documentation
WOWII Conjecture 6
For a connected graph G we have Ls(G) ≥ 1 + n(G) - m(G) - a(G) where a(G) is defined via independent sets.

L4DEL explanation
WOWII Conjecture 6 For a connected graph G we have Ls(G) ≥ 1 + n(G) - m(G) - a(G) where a(G) is defined via independent sets.
Sources and attribution: Pinned Lean source (1646ca16afd6)

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

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture6 (G : SimpleGraph α) [DecidableRel G.Adj] (h_conn : G.Connected) :
    1 + (Fintype.card α : ℝ) - matchingNumber G - α(G) ≤ Ls G := by
…
```