GraphConjecture181.lean`

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2 declarations, 1 contain sorry, 0 declared as axioms

Written on the Wall II - Conjecture 181

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

The expression deg_avg(B(G²)) is formalized by measuring degrees in G², the graph whose maximum-eccentricity vertices induce B(G²).

The conjecture is false for the triangular graph T(7) = L(K₇): it has at most 16 leaves in a spanning tree, largest induced bipartite subgraph order 6, and independence number 3. Its square is K₂₁, whose vertices all have degree 20, so the claimed inequality would give 22 ≥ 23.

Imports (1)

FormalConjecturesUtil

def WrittenOnTheWallII.GraphConjecture181.squarePeripheryAverage The average degree, in G², of the maximum-eccentricity vertices of G² line 43 source
Source documentation
The average degree, in G², of the maximum-eccentricity vertices of G².

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, Real
Proof uses: SimpleGraph.graphSquare, Finset, Finset.filter, Membership.mem, Set, SimpleGraph.maxEccentricityVertices, Classical.propDecidable, Finset.univ, HDiv.hDiv, Finset.sum, Finset.card, SimpleGraph.neighborFinset, SimpleGraph.neighborSet, SimpleGraph.Adj
9 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
noncomputable def squarePeripheryAverage {V : Type} [Fintype V] [DecidableEq V]
    (G : SimpleGraph V) : ℝ := by
…
```
theorem WrittenOnTheWallII.GraphConjecture181.conjecture181 sorry line 60 source
depends on sorry what this means
Statement uses: Iff, False, Fintype, DecidableEq, Nontrivial, SimpleGraph, DecidableRel, SimpleGraph.Adj, SimpleGraph.Connected, GE.ge, Real, HAdd.hAdd, SimpleGraph.Ls, SimpleGraph.b, SimpleGraph.indepNum, WrittenOnTheWallII.GraphConjecture181.squarePeripheryAverage
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
11 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.