GraphConjecture19.lean`

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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 19

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

Imports (1)

FormalConjecturesUtil

theorem WrittenOnTheWallII.GraphConjecture19.conjecture19 Documented declaration: conjecture19 sorry line 46 source
Source documentation
WOWII Conjecture 19
If G is connected then the size b(G) of a largest induced bipartite subgraph satisfies b(G) ≥ FLOOR((∑ ecc(v))/(|V|) + sSup (range (l G))), where ecc(v) denotes eccentricity and l(G) is the independence number of neighbourhoods.

L4DEL explanation
WOWII Conjecture 19 If G is connected then the size b(G) of a largest induced bipartite subgraph satisfies b(G) ≥ FLOOR((∑ ecc(v))/(|V|) + sSup (range (l G))), where ecc(v) denotes eccentricity and l(G) is the independence number of neighbourhoods.
Sources and attribution: Pinned Lean source (1646ca16afd6)

depends on sorry what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, Nontrivial, SimpleGraph.Connected, LE.le, Real, Int.floor, HAdd.hAdd, HDiv.hDiv, Finset.sum, Finset.univ, ENat.toNat, SimpleGraph.eccent, Fintype.card, SupSet.sSup, Set.range, SimpleGraph.indepNeighbors, SimpleGraph.b
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
31 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture19 (G : SimpleGraph α) [Nontrivial α] (h_conn : G.Connected) :
    ⌊(∑ v ∈ Finset.univ, ((G.eccent v).toNat : ℝ)) / (Fintype.card α : ℝ) +
      sSup (Set.range (indepNeighbors G))⌋ ≤ b G := by
…
```