GraphConjecture40.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 40

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

Imports (1)

FormalConjecturesUtil

theorem WrittenOnTheWallII.GraphConjecture40.conjecture40 Documented declaration: conjecture40 sorry line 44 source
Source documentation
WOWII Conjecture 40
For a nontrivial connected graph G the size f(G) of a largest induced forest satisfies f(G) ≥ ceil((p(G) + b(G) + 1)/2) where p(G) is the path cover number and b(G) is the largest induced bipartite subgraph size.

L4DEL explanation
WOWII Conjecture 40 For a nontrivial connected graph G the size f(G) of a largest induced forest satisfies f(G) ≥ ceil((p(G) + b(G) + 1)/2) where p(G) is the path cover number and b(G) is the largest induced bipartite subgraph size.
Sources and attribution: Pinned Lean source (1646ca16afd6)

depends on sorry what this means
Statement uses: Fintype, DecidableEq, Nontrivial, SimpleGraph, SimpleGraph.Connected, LT.lt, Nat, OfNat.ofNat, Fintype.card, LE.le, Int, Int.ceil, Real, HDiv.hDiv, HAdd.hAdd, SimpleGraph.pathCoverNumber, SimpleGraph.b, SimpleGraph.largestInducedForestSize
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
38 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture40 (h_conn : G.Connected) (h_nontrivial : 1 < Fintype.card α) :
    ⌈(((pathCoverNumber G : ℝ) + b G + 1) / 2)⌉ ≤  G.largestInducedForestSize := by
…
```